Kapustyan, Oleksiy; Kapustian, Olena; Korol, Ihor; Rubino, Bruno Attracting sets of impulse-perturbed heat equation in the space of continuous functions. (English) Zbl 07911218 Miskolc Math. Notes 25, No. 1, 317-327 (2024). MSC: 35B41 35K05 35R12 35Q79 PDFBibTeX XMLCite \textit{O. Kapustyan} et al., Miskolc Math. Notes 25, No. 1, 317--327 (2024; Zbl 07911218) Full Text: DOI
Kapustyan, Volodymyr; Pyshnograiev, Ivan Existence and uniqueness of solution for a parabolic-hyperbolic equation with multiplicative control and nonlocal boundary conditions. (English. Ukrainian original) Zbl 07906289 Ukr. Math. J. 76, No. 2, 280-301 (2024); translation from Ukr. Mat. Zh. 76, No. 2, 257-275 (2024). MSC: 35A01 35A02 PDFBibTeX XMLCite \textit{V. Kapustyan} and \textit{I. Pyshnograiev}, Ukr. Math. J. 76, No. 2, 280--301 (2024; Zbl 07906289); translation from Ukr. Mat. Zh. 76, No. 2, 257--275 (2024) Full Text: DOI
Kapustyan, O.; Yusypiv, T. Robust stability of the attractor of a nonlinear wave equation without uniqueness of the solution. (English. Ukrainian original) Zbl 1532.35081 J. Math. Sci., New York 274, No. 6, 850-860 (2023); translation from Neliniĭni Kolyvannya 25, No. 2-3, 198-206 (2022). MSC: 35B41 35L20 35L71 37L30 PDFBibTeX XMLCite \textit{O. Kapustyan} and \textit{T. Yusypiv}, J. Math. Sci., New York 274, No. 6, 850--860 (2023; Zbl 1532.35081); translation from Neliniĭni Kolyvannya 25, No. 2--3, 198--206 (2022) Full Text: DOI
Dashkovskiy, Sergey; Kapustyan, Oleksiy; Kapustian, Olena; Zhuk, Tetyana Asymptotic analysis of optimal control problems on the semiaxes for Carathéodory differential inclusions with fast oscillating coefficients. (English) Zbl 1529.49010 Nonlinear Anal., Model. Control 28, No. 6, 1077-1088 (2023). Reviewer: Alain Brillard (Riedisheim) MSC: 49K10 49K15 49J53 PDFBibTeX XMLCite \textit{S. Dashkovskiy} et al., Nonlinear Anal., Model. Control 28, No. 6, 1077--1088 (2023; Zbl 1529.49010) Full Text: Link
Kapustyan, Oleksiy; Kapustian, Olena; Korol, Ihor; Rubino, Bruno Uniform attractor of impulse-perturbed reaction-diffusion system. (English) Zbl 1527.35086 Math. Mech. Complex Syst. 11, No. 1, 45-55 (2023). MSC: 35B41 35K57 35Q79 35R12 PDFBibTeX XMLCite \textit{O. Kapustyan} et al., Math. Mech. Complex Syst. 11, No. 1, 45--55 (2023; Zbl 1527.35086) Full Text: DOI
Dashkovskiy, Sergey; Kapustyan, Oleksiy; Slynko, Vitalii Robust stability of a nonlinear ODE-PDE system. (English) Zbl 1518.35064 SIAM J. Control Optim. 61, No. 3, 1760-1777 (2023). MSC: 35B35 35K20 35K58 37L15 93D09 93D20 PDFBibTeX XMLCite \textit{S. Dashkovskiy} et al., SIAM J. Control Optim. 61, No. 3, 1760--1777 (2023; Zbl 1518.35064) Full Text: DOI arXiv
Kapustyan, O. V.; Yusypiv, T. V. Stability under perturbations for the attractor of a dissipative PDE-ODE-type system. (Stability under perturbations for the attractor of a dissipative PDF-ODF-type system.) (English. Ukrainian original) Zbl 1518.93117 J. Math. Sci., New York 272, No. 2, 236-243 (2023); translation from Neliniĭni Kolyvannya 24, No. 3, 336-341 (2021). Reviewer: Boris Ivanovich Konosevich (Donetsk) MSC: 93D25 93C15 93C20 35B41 34D45 PDFBibTeX XMLCite \textit{O. V. Kapustyan} and \textit{T. V. Yusypiv}, J. Math. Sci., New York 272, No. 2, 236--243 (2023; Zbl 1518.93117); translation from Neliniĭni Kolyvannya 24, No. 3, 336--341 (2021) Full Text: DOI
Kapustyan, Oleksiy; Kapustian, Olena; Stanzytskyi, Oleksandr; Korol, Ihor Uniform attractors in sup-norm for semi linear parabolic problem and application to the robust stability theory. (English) Zbl 07675589 Arch. Math. (Brno) 59, No. 2, 191-200 (2023). MSC: 34C10 PDFBibTeX XMLCite \textit{O. Kapustyan} et al., Arch. Math. (Brno) 59, No. 2, 191--200 (2023; Zbl 07675589) Full Text: DOI
Feketa, P.; Kapustyan, O. V.; Kapustian, O. A.; Korol, I. I. Global attractors of mild solutions semiflow for semilinear parabolic equation without uniqueness. (English) Zbl 1498.35099 Appl. Math. Lett. 135, Article ID 108435, 9 p. (2023). MSC: 35B41 35K20 35K58 PDFBibTeX XMLCite \textit{P. Feketa} et al., Appl. Math. Lett. 135, Article ID 108435, 9 p. (2023; Zbl 1498.35099) Full Text: DOI
Kapustyan, Oleksiy; Martynyuk, Olha; Misiats, Oleksandr; Stanzhytskyi, Oleksandr Long Time Behavior of Stochastic Thin Film Equation. arXiv:2311.16285 Preprint, arXiv:2311.16285 [math.AP] (2023). BibTeX Cite \textit{O. Kapustyan} et al., ``Long Time Behavior of Stochastic Thin Film Equation'', Preprint, arXiv:2311.16285 [math.AP] (2023) Full Text: arXiv OA License
Kapustyan, Oleksiy; Martynyuk, Olha; Misiats, Oleksandr; Stanzhytskyi, Oleksandr Thin Film Equations with Nonlinear Deterministic and Stochastic Perturbations. arXiv:2307.12665 Preprint, arXiv:2307.12665 [math.AP] (2023). BibTeX Cite \textit{O. Kapustyan} et al., ``Thin Film Equations with Nonlinear Deterministic and Stochastic Perturbations'', Preprint, arXiv:2307.12665 [math.AP] (2023) Full Text: arXiv OA License
Kapustyan, O. V.; Yusypiv, T. V. Stability of limit regimes in general reaction-diffusion type systems. (English) Zbl 07909368 Nauk. Visn. Uzhgorod. Univ., Ser. Mat. Inform. 41, No. 2, 48-60 (2022). MSC: 93C15 35B41 34D45 PDFBibTeX XMLCite \textit{O. V. Kapustyan} and \textit{T. V. Yusypiv}, Nauk. Visn. Uzhgorod. Univ., Ser. Mat. Inform. 41, No. 2, 48--60 (2022; Zbl 07909368) Full Text: DOI
Kapustyan, O. V.; Fedorenko, Yu. V.; Tsygansvs’ka, I. M. \(\omega\)-limit sets for impulsive-perturbed parabolic equation in the space of continuous functions. (Ukrainian. English summary) Zbl 1524.35089 Visn., Ser. Fiz.-Mat. Nauky, Kyïv. Univ. Im. Tarasa Shevchenka 2022, No. 4, 42-48 (2022). MSC: 35B41 35K20 35K58 PDFBibTeX XMLCite \textit{O. V. Kapustyan} et al., Visn., Ser. Fiz.-Mat. Nauky, Kyïv. Univ. Im. Tarasa Shevchenka 2022, No. 4, 42--48 (2022; Zbl 1524.35089) Full Text: DOI OA License
Kapustyan, O. V.; Stanzhytskyi, O. M.; Fartushny, I. D. Averaging method in the problem of optimal control for a perturbed parabolic equation. (English. Ukrainian original) Zbl 1504.35041 Ukr. Math. J. 74, No. 7, 1113-1120 (2022); translation from Ukr. Mat. Zh. 74, No. 7, 973-979 (2022). MSC: 35B27 35K20 35K58 35Q93 PDFBibTeX XMLCite \textit{O. V. Kapustyan} et al., Ukr. Math. J. 74, No. 7, 1113--1120 (2022; Zbl 1504.35041); translation from Ukr. Mat. Zh. 74, No. 7, 973--979 (2022) Full Text: DOI
Kapustyan, Oleksiy; Misiats, Oleksandr; Stanzhytskyi, Oleksandr Strong solutions and asymptotic behavior of bidomain equations with random noise. (English) Zbl 1498.35167 Stoch. Dyn. 22, No. 6, Article ID 2250027, 28 p. (2022). MSC: 35D35 35R60 35K51 35K58 60G10 60H15 PDFBibTeX XMLCite \textit{O. Kapustyan} et al., Stoch. Dyn. 22, No. 6, Article ID 2250027, 28 p. (2022; Zbl 1498.35167) Full Text: DOI arXiv
Dashkovskiy, Sergey; Kapustyan, Oleksiy Robustness of global attractors: abstract framework and application to dissipative wave equations. (English) Zbl 1498.35097 Evol. Equ. Control Theory 11, No. 5, 1565-1577 (2022). MSC: 35B41 35L20 35L71 35L90 93B35 93D09 35B35 PDFBibTeX XMLCite \textit{S. Dashkovskiy} and \textit{O. Kapustyan}, Evol. Equ. Control Theory 11, No. 5, 1565--1577 (2022; Zbl 1498.35097) Full Text: DOI
Schmid, Jochen; Kapustyan, Oleksiy; Dashkovskiy, Sergey Asymptotic gain results for attractors of semilinear systems. (English) Zbl 1505.37089 Math. Control Relat. Fields 12, No. 3, 763-788 (2022). MSC: 37L15 37L30 93C20 93D09 35B35 35B40 35B41 PDFBibTeX XMLCite \textit{J. Schmid} et al., Math. Control Relat. Fields 12, No. 3, 763--788 (2022; Zbl 1505.37089) Full Text: DOI arXiv
Gorban, N. V.; Kapustian, O. A.; Kapustyan, O. V. Approximate optimal controller for weakly nonlinear evolutionary equation of parabolic type. (English. Russian original) Zbl 1484.49005 Cybern. Syst. Anal. 57, No. 6, 883-888 (2021); translation from Kibern. Sist. Anal. 57, No. 6, 46-52 (2021). MSC: 49J20 35K55 47J35 PDFBibTeX XMLCite \textit{N. V. Gorban} et al., Cybern. Syst. Anal. 57, No. 6, 883--888 (2021; Zbl 1484.49005); translation from Kibern. Sist. Anal. 57, No. 6, 46--52 (2021) Full Text: DOI
Kapustyan, O. V.; Kurylko, O. B.; Yusypiv, T. V. Robust stability of the global attractor of the reaction-diffusion system. (Ukrainian. English summary) Zbl 1488.35098 Visn., Ser. Fiz.-Mat. Nauky, Kyïv. Univ. Im. Tarasa Shevchenka 2021, No. 3, 46-50 (2021). MSC: 35B41 37G35 37C70 PDFBibTeX XMLCite \textit{O. V. Kapustyan} et al., Visn., Ser. Fiz.-Mat. Nauky, Kyïv. Univ. Im. Tarasa Shevchenka 2021, No. 3, 46--50 (2021; Zbl 1488.35098) Full Text: DOI OA License
Dashkovskiy, Sergey; Kapustyan, Oleksiy; Perestyuk, Yuriy Stability of uniform attractors of impulsive multi-valued semiflows. (English) Zbl 1485.37021 Nonlinear Anal., Hybrid Syst. 40, Article ID 101025, 17 p. (2021). MSC: 37C75 37C70 37C10 PDFBibTeX XMLCite \textit{S. Dashkovskiy} et al., Nonlinear Anal., Hybrid Syst. 40, Article ID 101025, 17 p. (2021; Zbl 1485.37021) Full Text: DOI
Zgurovsky, Michael Z.; D’apice, Ciro; De Maio, Umberto; Gorban, Nataliia V.; Kasyanov, Pavlo O.; Kapustyan, Oleksiy V.; et al. Uniform global attractor for a class of nonautonomous evolution hemivariational inequalities with multidimensional “reaction-velocity” law. (English) Zbl 1479.35134 Sadovnichiy, Victor A. (ed.) et al., Contemporary approaches and methods in fundamental mathematics and mechanics. Cham: Springer. Underst. Complex Syst., 347-368 (2021). MSC: 35B41 47J20 47J22 PDFBibTeX XMLCite \textit{M. Z. Zgurovsky} et al., in: Contemporary approaches and methods in fundamental mathematics and mechanics. Cham: Springer. 347--368 (2021; Zbl 1479.35134) Full Text: DOI
Kapustyan, O. V.; Asrorov, F. A.; Sobchuk, V. V. Uniform attractor for an \(N\)-dimensional parabolic system with impulsive perturbation. (English. Ukrainian original) Zbl 1465.37088 J. Math. Sci., New York 254, No. 2, 219-228 (2021); translation from Neliniĭni Kolyvannya 22, No. 4, 474-481 (2019). MSC: 37L30 37L50 PDFBibTeX XMLCite \textit{O. V. Kapustyan} et al., J. Math. Sci., New York 254, No. 2, 219--228 (2021; Zbl 1465.37088); translation from Neliniĭni Kolyvannya 22, No. 4, 474--481 (2019) Full Text: DOI
Kapustyan, Oleksiy V.; Kasyanov, Pavlo O.; Taranets, Roman M. Strong solutions and trajectory attractors to the thin-film equation with absorption. (English) Zbl 1451.35030 J. Math. Anal. Appl. 493, No. 2, Article ID 124562, 15 p. (2021). MSC: 35B41 76A20 35K35 35K59 35D35 PDFBibTeX XMLCite \textit{O. V. Kapustyan} et al., J. Math. Anal. Appl. 493, No. 2, Article ID 124562, 15 p. (2021; Zbl 1451.35030) Full Text: DOI
Dashkovskiy, Sergey; Kapustyan, Oleksiy; Schmid, Jochen A local input-to-state stability result w.r.t. attractors of nonlinear reaction-diffusion equations. (English) Zbl 1455.93170 Math. Control Signals Syst. 32, No. 3, 309-326 (2020). MSC: 93D25 93C20 35K57 93C10 PDFBibTeX XMLCite \textit{S. Dashkovskiy} et al., Math. Control Signals Syst. 32, No. 3, 309--326 (2020; Zbl 1455.93170) Full Text: DOI arXiv OA License
Kapustyan, Olexiy V.; Kasyanov, Pavlo O.; Valero, José Chain recurrence and structure of \(\omega\)-limit sets of multivalued semiflows. (English) Zbl 1446.37017 Commun. Pure Appl. Anal. 19, No. 4, 2197-2217 (2020). MSC: 37B20 35B40 35B41 35K20 35R70 37B25 58C06 PDFBibTeX XMLCite \textit{O. V. Kapustyan} et al., Commun. Pure Appl. Anal. 19, No. 4, 2197--2217 (2020; Zbl 1446.37017) Full Text: DOI
Kapustyan, O. V.; Asrorov, F. A.; Perestyuk, Yu. M. On the exponential stability of a trivial torus for one class of nonlinear impulsive systems. (English. Ukrainian original) Zbl 1416.37029 J. Math. Sci., New York 238, No. 3, 263-270 (2019); translation from Neliniĭni Kolyvannya 20, No. 4, 502-508 (2017). MSC: 37C75 34A37 PDFBibTeX XMLCite \textit{O. V. Kapustyan} et al., J. Math. Sci., New York 238, No. 3, 263--270 (2019; Zbl 1416.37029); translation from Neliniĭni Kolyvannya 20, No. 4, 502--508 (2017) Full Text: DOI
Kapustyan, Volodymyr O.; Pyshnograiev, Ivan O. Divided optimal control for parabolic-hyperbolic equation with non-local pointed boundary conditions and quadratic quality criterion. (English) Zbl 1416.49041 Sadovnichiy, Victor A. (ed.) et al., Modern mathematics and mechanics. Fundamentals, problems and challenges. Cham: Springer. Underst. Complex Syst., 493-504 (2019). MSC: 49N10 35M33 49J20 49K20 35Q93 PDFBibTeX XMLCite \textit{V. O. Kapustyan} and \textit{I. O. Pyshnograiev}, in: Modern mathematics and mechanics. Fundamentals, problems and challenges. Cham: Springer. 493--504 (2019; Zbl 1416.49041) Full Text: DOI
Dashkovskiy, Sergey; Feketa, Petro; Kapustyan, Oleksiy V.; Romaniuk, Iryna V. Existence and invariance of global attractors for impulsive parabolic system without uniqueness. (English) Zbl 1416.35045 Sadovnichiy, Victor A. (ed.) et al., Modern mathematics and mechanics. Fundamentals, problems and challenges. Cham: Springer. Underst. Complex Syst., 57-78 (2019). MSC: 35B41 35R12 35K10 PDFBibTeX XMLCite \textit{S. Dashkovskiy} et al., in: Modern mathematics and mechanics. Fundamentals, problems and challenges. Cham: Springer. 57--78 (2019; Zbl 1416.35045) Full Text: DOI
Kapustyan, O. V.; Romanyuk, I. V. Global attractor of an impulsive dynamical system generated by the wave equation. (English. Ukrainian original) Zbl 1414.35035 J. Math. Sci., New York 236, No. 3, 300-312 (2019); translation from Neliniĭni Kolyvannya 20, No. 3, 361-372 (2017). MSC: 35B41 35R12 35L90 PDFBibTeX XMLCite \textit{O. V. Kapustyan} and \textit{I. V. Romanyuk}, J. Math. Sci., New York 236, No. 3, 300--312 (2019; Zbl 1414.35035); translation from Neliniĭni Kolyvannya 20, No. 3, 361--372 (2017) Full Text: DOI
Kapustyan, Volodymyr O.; Pyshnograiev, Ivan O.; Kapustian, Olena A. Quasi-optimal control with a general quadratic criterion in a special norm for systems described by parabolic-hyperbolic equations with non-local boundary conditions. (English) Zbl 1417.49022 Discrete Contin. Dyn. Syst., Ser. B 24, No. 3, 1243-1258 (2019). Reviewer: Yekini Shehu (Nsukka) MSC: 49K20 PDFBibTeX XMLCite \textit{V. O. Kapustyan} et al., Discrete Contin. Dyn. Syst., Ser. B 24, No. 3, 1243--1258 (2019; Zbl 1417.49022) Full Text: DOI
Kapustyan, Olexiy V.; Kasyanov, Pavlo O.; Valero, José; Zgurovsky, Mikhail Z. Attractors of multivalued semi-flows generated by solutions of optimal control problems. (English) Zbl 1473.35060 Discrete Contin. Dyn. Syst., Ser. B 24, No. 3, 1229-1242 (2019). Reviewer: Bixiang Wang (Socorro) MSC: 35B41 35B40 35K55 35Q30 35Q35 37B25 58C06 35Q93 PDFBibTeX XMLCite \textit{O. V. Kapustyan} et al., Discrete Contin. Dyn. Syst., Ser. B 24, No. 3, 1229--1242 (2019; Zbl 1473.35060) Full Text: DOI
Garrido, Tomás Caraballo (ed.); Kapustyan, Oleksiy V. (ed.); Kasyanov, Pavlo O. (ed.); Valero, José (ed.); Zgurovsky, Michael (ed.) Preface to the special issue “Dynamics and control in distributed systems: dedicated to the memory of Valery S. Melnik (1952–2007)”. (English) Zbl 1410.00024 Discrete Contin. Dyn. Syst., Ser. B 24, No. 3, i-v (2019). MSC: 00B15 35-06 37-06 49-06 01A70 PDFBibTeX XMLCite \textit{T. C. Garrido} (ed.) et al., Discrete Contin. Dyn. Syst., Ser. B 24, No. 3, i-v (2019; Zbl 1410.00024) Full Text: DOI
Kapustyan, O. V.; Perestyuk, M. O.; Romanyuk, I. V. Stability of global attractors of impulsive infinite-dimensional systems. (English. Ukrainian original) Zbl 1427.35343 Ukr. Math. J. 70, No. 1, 30-41 (2018); translation from Ukr. Mat. Zh. 70, No. 1, 29-39 (2018). MSC: 35R12 37C75 35B25 35B41 35K91 PDFBibTeX XMLCite \textit{O. V. Kapustyan} et al., Ukr. Math. J. 70, No. 1, 30--41 (2018; Zbl 1427.35343); translation from Ukr. Mat. Zh. 70, No. 1, 29--39 (2018) Full Text: DOI
Kapustyan, Oleksiy V.; Kasyanov, Pavlo O.; Valero, José; Zgurovsky, Michael Z. Strong attractors for vanishing viscosity approximations of non-Newtonian suspension flows. (English) Zbl 1411.35046 Discrete Contin. Dyn. Syst., Ser. B 23, No. 3, 1155-1176 (2018). Reviewer: Jörg Härterich (Bochum) MSC: 35B41 35B40 35K55 76A05 37B25 37L05 PDFBibTeX XMLCite \textit{O. V. Kapustyan} et al., Discrete Contin. Dyn. Syst., Ser. B 23, No. 3, 1155--1176 (2018; Zbl 1411.35046) Full Text: DOI
Dashkovskiy, Sergey; Feketa, Petro; Kapustyan, Oleksiy; Romaniuk, Iryna Invariance and stability of global attractors for multi-valued impulsive dynamical systems. (English) Zbl 1378.37120 J. Math. Anal. Appl. 458, No. 1, 193-218 (2018). MSC: 37L15 34D45 34A37 37L30 PDFBibTeX XMLCite \textit{S. Dashkovskiy} et al., J. Math. Anal. Appl. 458, No. 1, 193--218 (2018; Zbl 1378.37120) Full Text: DOI
Kapustyan, Oleksiy; Perestyuk, Mykola; Romaniuk, Iryna Global attractor of a weakly nonlinear parabolic system with discontinuous trajectories. (English) Zbl 1390.35028 Mem. Differ. Equ. Math. Phys. 72, 59-70 (2017). MSC: 35B41 35B40 35K55 37B25 58C06 PDFBibTeX XMLCite \textit{O. Kapustyan} et al., Mem. Differ. Equ. Math. Phys. 72, 59--70 (2017; Zbl 1390.35028) Full Text: Link
Perestyuk, M. O.; Kapustyan, O. V.; Romanyuk, I. V. Global attractor of an impulsive parabolic system. (Ukrainian. English summary) Zbl 1389.35089 Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 2017, No. 5, 3-7 (2017). MSC: 35B41 35B20 35K99 PDFBibTeX XMLCite \textit{M. O. Perestyuk} et al., Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 2017, No. 5, 3--7 (2017; Zbl 1389.35089) Full Text: DOI OA License
Garrido-Atienza, María J. (ed.); Kapustyan, Oleksiy V. (ed.); Valero, José (ed.) Preface to the special issue “Finite and infinite dimensional multivalued dynamical systems”. (English) Zbl 1359.00022 Discrete Contin. Dyn. Syst., Ser. B 22, No. 5, i-iv (2017). MSC: 00B15 35-06 37-06 PDFBibTeX XMLCite \textit{M. J. Garrido-Atienza} (ed.) et al., Discrete Contin. Dyn. Syst., Ser. B 22, No. 5, i-iv (2017; Zbl 1359.00022) Full Text: DOI
Valero, José; Kasyanov, Pavlo O.; Kapustyan, Oleksiy V. Regularity of global attractors for reaction-diffusion systems with no more than quadratic growth. (English) Zbl 1359.35011 Discrete Contin. Dyn. Syst., Ser. B 22, No. 5, 1899-1908 (2017). MSC: 35B40 35B41 35K55 35Q30 35Q35 37B25 58C06 PDFBibTeX XMLCite \textit{J. Valero} et al., Discrete Contin. Dyn. Syst., Ser. B 22, No. 5, 1899--1908 (2017; Zbl 1359.35011) Full Text: DOI
Dashkovskiy, Sergey; Kapustyan, Oleksiy; Romaniuk, Iryna Global attractors of impulsive parabolic inclusions. (English) Zbl 1359.35010 Discrete Contin. Dyn. Syst., Ser. B 22, No. 5, 1875-1886 (2017). MSC: 35B40 35B41 35K55 58C06 PDFBibTeX XMLCite \textit{S. Dashkovskiy} et al., Discrete Contin. Dyn. Syst., Ser. B 22, No. 5, 1875--1886 (2017; Zbl 1359.35010) Full Text: DOI
Kapustyan, O. V.; Perestyuk, M. O. Global attractors in impulsive infinite-dimensional systems. (English. Russian original) Zbl 1490.37094 Ukr. Math. J. 68, No. 4, 583-597 (2016); translation from Ukr. Mat. Zh. 68, No. 4, 517-528 (2016). MSC: 37L30 35B20 35R12 PDFBibTeX XMLCite \textit{O. V. Kapustyan} and \textit{M. O. Perestyuk}, Ukr. Math. J. 68, No. 4, 583--597 (2016; Zbl 1490.37094); translation from Ukr. Mat. Zh. 68, No. 4, 517--528 (2016) Full Text: DOI
Kapustyan, V. E.; Pyshnograev, I. A. Problem of optimal control for parabolic-hyperbolic equations with nonlocal point boundary conditions and semidefinite quality criterion. (English. Ukrainian original) Zbl 1381.49020 Ukr. Math. J. 67, No. 8, 1204-1218 (2016); translation from Ukr. Mat. Zh. 67, No. 8, 1068-1081 (2015). MSC: 49K20 49J45 PDFBibTeX XMLCite \textit{V. E. Kapustyan} and \textit{I. A. Pyshnograev}, Ukr. Math. J. 67, No. 8, 1204--1218 (2016; Zbl 1381.49020); translation from Ukr. Mat. Zh. 67, No. 8, 1068--1081 (2015) Full Text: DOI
Kapustyan, O. V.; Romanyuk, I. V. The existence of global attractor for second order evolution equation with discontinuous trajectories. (Ukrainian. English summary) Zbl 1389.34189 Visn., Ser. Fiz.-Mat. Nauky, Kyïv. Univ. Im. Tarasa Shevchenka 2016, No. 4, 29-32 (2016). MSC: 34G25 34A37 34D45 34D05 PDFBibTeX XMLCite \textit{O. V. Kapustyan} and \textit{I. V. Romanyuk}, Visn., Ser. Fiz.-Mat. Nauky, Kyïv. Univ. Im. Tarasa Shevchenka 2016, No. 4, 29--32 (2016; Zbl 1389.34189)
Kapustyan, O. A. Approximate synthesis for distributed optimal control problem with Nemyckiĭ type cost functional. (Ukrainian. English summary) Zbl 1374.49037 Visn., Ser. Fiz.-Mat. Nauky, Kyïv. Univ. Im. Tarasa Shevchenka 2016, No. 3, 73-78 (2016). MSC: 49N35 49J20 93B50 PDFBibTeX XMLCite \textit{O. A. Kapustyan}, Visn., Ser. Fiz.-Mat. Nauky, Kyïv. Univ. Im. Tarasa Shevchenka 2016, No. 3, 73--78 (2016; Zbl 1374.49037)
Kapustyan, Oleksiy V.; Rusina, Alina V. On approximate regulator in linear-quadratic problem with distributed control and rapidly oscillating parameters. (English) Zbl 1366.49024 Sadovnichiy, Victor A. (ed.) et al., Advances in dynamical systems and control. Cham: Springer (ISBN 978-3-319-40672-5/hbk; 978-3-319-40673-2/ebook). Studies in Systems, Decision and Control 69, 403-415 (2016). Reviewer: Dian K. Palagachev (Bari) MSC: 49K20 49N10 35K20 PDFBibTeX XMLCite \textit{O. V. Kapustyan} and \textit{A. V. Rusina}, Stud. Syst. Decis. Control 69, 403--415 (2016; Zbl 1366.49024) Full Text: DOI
Kapustyan, Volodymyr O.; Pyshnograiev, Ivan O. Approximate optimal control for parabolic-hyperbolic equations with nonlocal boundary conditions and general quadratic quality criterion. (English) Zbl 1366.49025 Sadovnichiy, Victor A. (ed.) et al., Advances in dynamical systems and control. Cham: Springer (ISBN 978-3-319-40672-5/hbk; 978-3-319-40673-2/ebook). Studies in Systems, Decision and Control 69, 387-401 (2016). Reviewer: Dian K. Palagachev (Bari) MSC: 49K20 PDFBibTeX XMLCite \textit{V. O. Kapustyan} and \textit{I. O. Pyshnograiev}, Stud. Syst. Decis. Control 69, 387--401 (2016; Zbl 1366.49025) Full Text: DOI
Kapustyan, Oleksiy V.; Romaniuk, Iryna V. Global attractors for discontinuous dynamical systems with multi-valued impulsive perturbations. (English) Zbl 1362.37152 Sadovnichiy, Victor A. (ed.) et al., Advances in dynamical systems and control. Cham: Springer (ISBN 978-3-319-40672-5/hbk; 978-3-319-40673-2/ebook). Studies in Systems, Decision and Control 69, 197-210 (2016). MSC: 37L30 34A37 35R12 PDFBibTeX XMLCite \textit{O. V. Kapustyan} and \textit{I. V. Romaniuk}, Stud. Syst. Decis. Control 69, 197--210 (2016; Zbl 1362.37152) Full Text: DOI
Valero, J.; Giménez, A.; Kapustyan, O. V.; Kasyanov, P. O.; Amigó, J. M. Convergence of equilibria for numerical approximations of a suspension model. (English) Zbl 1404.76015 Comput. Math. Appl. 72, No. 4, 856-878 (2016). MSC: 76A05 65M12 65M06 76M20 76T20 PDFBibTeX XMLCite \textit{J. Valero} et al., Comput. Math. Appl. 72, No. 4, 856--878 (2016; Zbl 1404.76015) Full Text: DOI
Kapustyan, O. V.; Rusina, A. V. Approximate synthesis of distributed bounded control for a parabolic problem with rapidly oscillating coefficients. (English. Ukrainian original) Zbl 1348.49030 Ukr. Math. J. 67, No. 3, 408-420 (2015); translation from Ukr. Mat. Zh. 67, No. 3, 355-365 (2015). MSC: 49N35 49N10 49J20 35K10 PDFBibTeX XMLCite \textit{O. V. Kapustyan} and \textit{A. V. Rusina}, Ukr. Math. J. 67, No. 3, 408--420 (2015; Zbl 1348.49030); translation from Ukr. Mat. Zh. 67, No. 3, 355--365 (2015) Full Text: DOI
Kapustyan, O. V.; Perestyuk, M. O. Existence of global attractors for impulsive dynamical systems. (Ukrainian. English summary) Zbl 1363.35375 Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 2015, No. 12, 13-18 (2015). MSC: 35R12 35B41 35K99 PDFBibTeX XMLCite \textit{O. V. Kapustyan} and \textit{M. O. Perestyuk}, Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 2015, No. 12, 13--18 (2015; Zbl 1363.35375) Full Text: DOI OA License
Kapustyan, V. O.; Kapustian, O. A.; Kapustyan, O. V.; Mazur, O. K. The optimal control problem for parabolic equation with nonlocal boundary conditions in circular sector. (English) Zbl 1335.49013 Sadovnichiy, Viktor A. (ed.) et al., Continuous and distributed systems II. Theory and applications. Cham: Springer (ISBN 978-3-319-19074-7/hbk; 978-3-319-19075-4/ebook). Studies in Systems, Decision and Control 30, 297-314 (2015). MSC: 49J20 49N10 35K20 PDFBibTeX XMLCite \textit{V. O. Kapustyan} et al., Stud. Syst. Decis. Control 30, 297--314 (2015; Zbl 1335.49013) Full Text: DOI
Kapustyan, V. O.; Pyshnograiev, I. O. Minimax estimates for solutions of parabolic-hyperbolic equations with nonlocal boundary conditions. (English) Zbl 1335.93035 Sadovnichiy, Viktor A. (ed.) et al., Continuous and distributed systems II. Theory and applications. Cham: Springer (ISBN 978-3-319-19074-7/hbk; 978-3-319-19075-4/ebook). Studies in Systems, Decision and Control 30, 277-296 (2015). MSC: 93B30 35R09 35M11 PDFBibTeX XMLCite \textit{V. O. Kapustyan} and \textit{I. O. Pyshnograiev}, Stud. Syst. Decis. Control 30, 277--296 (2015; Zbl 1335.93035) Full Text: DOI
Kapustyan, O. V.; Valero, J.; Kasyanov, P. O.; Giménez, A.; Amigó, J. M. Convergence of numerical approximations for a non-Newtonian model of suspensions. (English) Zbl 1334.65131 Int. J. Bifurcation Chaos Appl. Sci. Eng. 25, No. 14, Article ID 1540022, 24 p. (2015). MSC: 65M06 76T20 35K10 PDFBibTeX XMLCite \textit{O. V. Kapustyan} et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 25, No. 14, Article ID 1540022, 24 p. (2015; Zbl 1334.65131) Full Text: DOI
Kapustyan, V. O.; Pyshnograiev, I. O. Distributed control with the general quadratic criterion in a special norm for systems described by parabolic-hyperbolic equations with nonlocal boundary conditions. (English. Russian original) Zbl 1327.93227 Cybern. Syst. Anal. 51, No. 3, 438-447 (2015); translation from Kibern. Sist. Anal. 2015, No. 3, 132-142 (2015). MSC: 93C20 35Q93 49K20 PDFBibTeX XMLCite \textit{V. O. Kapustyan} and \textit{I. O. Pyshnograiev}, Cybern. Syst. Anal. 51, No. 3, 438--447 (2015; Zbl 1327.93227); translation from Kibern. Sist. Anal. 2015, No. 3, 132--142 (2015) Full Text: DOI
Blizorukova, M. S.; Kapustyan, V. E.; Maksimov, V. I. Application of feedback control methods to two models in environmental economics. (English. Russian original) Zbl 1332.91083 Comput. Math. Model. 25, No. 4, 459-469 (2014); translation from Prikl. Mat. Inf. 44, 22-34 (2013). MSC: 91B76 49N25 93B52 PDFBibTeX XMLCite \textit{M. S. Blizorukova} et al., Comput. Math. Model. 25, No. 4, 459--469 (2014; Zbl 1332.91083); translation from Prikl. Mat. Inf. 44, 22--34 (2013) Full Text: DOI
Kapustyan, V. O.; Kapustian, O. A.; Mazur, O. K. Distributed optimal control in one non-self-adjoint boundary value problem. (English) Zbl 1323.49003 Zgurovsky, Mikhail Z. (ed.) et al., Continuous and distributed systems. Theory and applications. Cham: Springer (ISBN 978-3-319-03145-3/hbk; 978-3-319-03146-0/ebook). Solid Mechanics and Its Applications 211, 303-312 (2014). MSC: 49J20 35J25 PDFBibTeX XMLCite \textit{V. O. Kapustyan} et al., Solid Mech. Appl. 211, 303--312 (2014; Zbl 1323.49003) Full Text: DOI
Gorban, Nataliia V.; Kapustyan, Oleksiy V.; Kasyanov, Pavlo O.; Paliichuk, Liliia S. On global attractors for autonomous damped wave equation with discontinuous nonlinearity. (English) Zbl 1327.35232 Zgurovsky, Mikhail Z. (ed.) et al., Continuous and distributed systems. Theory and applications. Cham: Springer (ISBN 978-3-319-03145-3/hbk; 978-3-319-03146-0/ebook). Solid Mechanics and Its Applications 211, 221-237 (2014). MSC: 35L05 35B41 PDFBibTeX XMLCite \textit{N. V. Gorban} et al., Solid Mech. Appl. 211, 221--237 (2014; Zbl 1327.35232) Full Text: DOI
Kapustyan, Oleksiy V.; Kasyanov, Pavlo O.; Valero, José; Zgurovsky, Mikhail Z. Structure of uniform global attractor for general non-autonomous reaction-diffusion system. (English) Zbl 1323.35084 Zgurovsky, Mikhail Z. (ed.) et al., Continuous and distributed systems. Theory and applications. Cham: Springer (ISBN 978-3-319-03145-3/hbk; 978-3-319-03146-0/ebook). Solid Mechanics and Its Applications 211, 163-180 (2014). MSC: 35K57 35B41 PDFBibTeX XMLCite \textit{O. V. Kapustyan} et al., Solid Mech. Appl. 211, 163--180 (2014; Zbl 1323.35084) Full Text: DOI
Kapustyan, O. A.; Mazur, O. K. Approximate optimal control for Poisson equation with nonlocal boundary conditions. (Ukrainian. English summary) Zbl 1324.49027 Visn., Ser. Fiz.-Mat. Nauky, Kyïv. Univ. Im. Tarasa Shevchenka 2014, No. 3, 130-134 (2014). MSC: 49M30 49J20 35J05 PDFBibTeX XMLCite \textit{O. A. Kapustyan} and \textit{O. K. Mazur}, Visn., Ser. Fiz.-Mat. Nauky, Kyïv. Univ. Im. Tarasa Shevchenka 2014, No. 3, 130--134 (2014; Zbl 1324.49027)
Kapustyan, V. O.; Kapustyan, O. A.; Mazur, O. K. Problem of optimal control for the Poisson equation with nonlocal boundary conditions. (English. Ukrainian original) Zbl 1308.49006 J. Math. Sci., New York 201, No. 3, 325-334 (2014); translation from Neliniĭni Kolyvannya 16, No. 3, 350-358 (2013). MSC: 49J20 35J05 PDFBibTeX XMLCite \textit{V. O. Kapustyan} et al., J. Math. Sci., New York 201, No. 3, 325--334 (2014; Zbl 1308.49006); translation from Neliniĭni Kolyvannya 16, No. 3, 350--358 (2013) Full Text: DOI
Kapustyan, O. V.; Kapustyan, O. A.; Rusina, A. V. Approximate synthesis in distributed impulsive optimal control problem with quickly-oscillating coefficients. (Ukrainian. English summary) Zbl 1313.49041 Visn., Ser. Fiz.-Mat. Nauky, Kyïv. Univ. Im. Tarasa Shevchenka 2014, No. 2, 61-66 (2014). MSC: 49N25 49J30 49K20 93B50 PDFBibTeX XMLCite \textit{O. V. Kapustyan} et al., Visn., Ser. Fiz.-Mat. Nauky, Kyïv. Univ. Im. Tarasa Shevchenka 2014, No. 2, 61--66 (2014; Zbl 1313.49041)
Kapustyan, Oleksiy V.; Kasyanov, Pavlo O.; Valero, José Regular solutions and global attractors for reaction-diffusion systems without uniqueness. (English) Zbl 1304.35119 Commun. Pure Appl. Anal. 13, No. 5, 1891-1906 (2014). MSC: 35B41 35B40 35K55 37B25 58C06 35K57 PDFBibTeX XMLCite \textit{O. V. Kapustyan} et al., Commun. Pure Appl. Anal. 13, No. 5, 1891--1906 (2014; Zbl 1304.35119) Full Text: DOI OA License
Kapustyan, Oleksiy V.; Kasyanov, Pavlo O.; Valero, José Structure and regularity of the global attractor of a reaction-diffusion equation with non-smooth nonlinear term. (English) Zbl 1304.35118 Discrete Contin. Dyn. Syst. 34, No. 10, 4155-4182 (2014). MSC: 35B41 35B40 35K55 37L25 58C06 35K57 PDFBibTeX XMLCite \textit{O. V. Kapustyan} et al., Discrete Contin. Dyn. Syst. 34, No. 10, 4155--4182 (2014; Zbl 1304.35118) Full Text: DOI arXiv
Kapustyan, V. E.; Lazarenko, I. S. Parametric optimal synthesis for a parabolic equation with nonlocal boundary conditions and semidefinite functional. (English. Russian original) Zbl 1301.49012 J. Math. Sci., New York 197, No. 1, 39-44 (2014); translation from Neliniĭni Kolyvannya 16, No. 1, 38-43 (2013). MSC: 49J20 49N35 93B52 PDFBibTeX XMLCite \textit{V. E. Kapustyan} and \textit{I. S. Lazarenko}, J. Math. Sci., New York 197, No. 1, 39--44 (2014; Zbl 1301.49012); translation from Neliniĭni Kolyvannya 16, No. 1, 38--43 (2013) Full Text: DOI
Kapustyan, Vladimir; Maksimov, Vyacheslav On attaining the prescribed quality of a controlled fourth order system. (English) Zbl 1292.93064 Int. J. Appl. Math. Comput. Sci. 24, No. 1, 75-85 (2014). MSC: 93B52 93A30 93B35 PDFBibTeX XMLCite \textit{V. Kapustyan} and \textit{V. Maksimov}, Int. J. Appl. Math. Comput. Sci. 24, No. 1, 75--85 (2014; Zbl 1292.93064) Full Text: DOI
Kapustyan, O. V.; Pankov, A. V. Global \(\varphi\)-attractor for a modified 3D Bénard system on channel-like domains. (English) Zbl 1288.35081 Nonauton. Dyn. Syst. 1, 1-9 (2014). MSC: 35B40 35B41 35K55 35Q30 35Q35 37B25 58C06 PDFBibTeX XMLCite \textit{O. V. Kapustyan} and \textit{A. V. Pankov}, Nonauton. Dyn. Syst. 1, 1--9 (2014; Zbl 1288.35081) Full Text: DOI OA License
Gorban, Nataliia V.; Kapustyan, Oleksiy V.; Kasyanov, Pavlo O. Uniform trajectory attractor for non-autonomous reaction-diffusion equations with Carathéodory’s nonlinearity. (English) Zbl 1286.35045 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 98, 13-26 (2014). MSC: 35B41 35K57 PDFBibTeX XMLCite \textit{N. V. Gorban} et al., Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 98, 13--26 (2014; Zbl 1286.35045) Full Text: DOI
Kapustyan, O. A. Investigation of solutions dynamics of optimal control problem for parabolic equation. (Ukrainian. English summary) Zbl 1313.35154 Visn., Ser. Fiz.-Mat. Nauky, Kyïv. Univ. Im. Tarasa Shevchenka 2013, No. 4, 118-121 (2013). MSC: 35K55 35B41 35Q99 PDFBibTeX XMLCite \textit{O. A. Kapustyan}, Visn., Ser. Fiz.-Mat. Nauky, Kyïv. Univ. Im. Tarasa Shevchenka 2013, No. 4, 118--121 (2013; Zbl 1313.35154)
Kapustyan, O. V.; Pankov, A. V. Global \(\varphi\)-attractor for a modified 3D Bénard system on channel-like domains. (English) Zbl 1276.35038 Nonauton. Stoch. Dyn. Syst. 1, 1-9 (2013). MSC: 35B41 35B40 35K55 35Q30 35Q35 37B25 58C06 PDFBibTeX XMLCite \textit{O. V. Kapustyan} and \textit{A. V. Pankov}, Nonauton. Stoch. Dyn. Syst. 1, 1--9 (2013; Zbl 1276.35038) Full Text: DOI OA License
Kapustyan, O. V.; Pan’kov, A. V.; Valero, J. On the existence and connectedness of a global attractor for solutions of the three-dimensional Bénard system that satisfy a system of energy inequalities. (English. Russian original) Zbl 1291.35222 J. Math. Sci., New York 191, No. 3, 388-402 (2013); translation from Neliniĭni Kolyvannya 15, No. 3, 354-366 (2012). MSC: 35Q35 35B41 PDFBibTeX XMLCite \textit{O. V. Kapustyan} et al., J. Math. Sci., New York 191, No. 3, 388--402 (2013; Zbl 1291.35222); translation from Neliniĭni Kolyvannya 15, No. 3, 354--366 (2012) Full Text: DOI
Kapustyan, Oleksiy V.; Kapustyan, Olena A.; Sukretna, Anna V. Approximate bounded synthesis for distributed systems. (English) Zbl 1324.68001 Saarbrücken: LAP Lambert Academic Publishing (ISBN 978-3-659-32021-7). 236 p. (2013). Reviewer: Mikhail P. Moklyachuk (Kyïv) MSC: 68-02 68M14 68Q25 68Q55 68Q85 68T05 68W10 PDFBibTeX XMLCite \textit{O. V. Kapustyan} et al., Approximate bounded synthesis for distributed systems. Saarbrücken: LAP Lambert Academic Publishing (2013; Zbl 1324.68001)
Perestyuk, Mykola; Kapustyan, Oleksiy Long-time behavior of evolution inclusion with non-damped impulsive effects. (English) Zbl 1300.34147 Mem. Differ. Equ. Math. Phys. 56, 89-113 (2012). MSC: 34G25 34A37 34D05 34D45 PDFBibTeX XMLCite \textit{M. Perestyuk} and \textit{O. Kapustyan}, Mem. Differ. Equ. Math. Phys. 56, 89--113 (2012; Zbl 1300.34147)
Kapustyan, O. V.; Shklyar, T. B. Global attractor of a parabolic inclusion with nonautonomous main part. (English. Russian original) Zbl 1323.37045 J. Math. Sci., New York 187, No. 4, 458-470 (2012); translation from Neliniĭni Kolyvannya 15, No. 1, 77-88 (2012). MSC: 37L30 35B41 35K90 PDFBibTeX XMLCite \textit{O. V. Kapustyan} and \textit{T. B. Shklyar}, J. Math. Sci., New York 187, No. 4, 458--470 (2012; Zbl 1323.37045); translation from Neliniĭni Kolyvannya 15, No. 1, 77--88 (2012) Full Text: DOI
Kapustyan, Alexey V.; Pankov, Andrey V.; Valero, José Erratum to: On global attractors of multivalued semiflows generated by the 3D Bénard system. (English) Zbl 1255.35044 Set-Valued Var. Anal. 20, No. 4, 667-667 (2012). MSC: 35B40 35B41 35K55 35Q30 35Q35 37B25 58C06 PDFBibTeX XMLCite \textit{A. V. Kapustyan} et al., Set-Valued Var. Anal. 20, No. 4, 667--667 (2012; Zbl 1255.35044) Full Text: DOI
Kapustyan, Alexey V.; Pankov, Andrey V.; Valero, José On global attractors of multivalued semiflows generated by the 3D Bénard system. (English) Zbl 1259.35042 Set-Valued Var. Anal. 20, No. 3, 445-465 (2012); erratum ibid. 20, No. 4, 667-667 (2012). Reviewer: Cheng He (Beijing) MSC: 35B41 35B40 35Q35 37B25 PDFBibTeX XMLCite \textit{A. V. Kapustyan} et al., Set-Valued Var. Anal. 20, No. 3, 445--465 (2012; Zbl 1259.35042) Full Text: DOI
Zgurovsky, Mikhail Z.; Kasyanov, Pavlo O.; Kapustyan, Oleksiy V.; Valero, José; Zadoianchuk, Nina V. Evolution inclusions and variation inequalities for earth data processing. III. Long-time behavior of evolution inclusions solutions in earth data analysis. (English) Zbl 1317.86003 Advances in Mechanics and Mathematics 27. Berlin: Springer (ISBN 978-3-642-28511-0/hbk; 978-3-642-28512-7/ebook). xli, 330 p. (2012). MSC: 86-02 86A04 86A30 00A69 PDFBibTeX XMLCite \textit{M. Z. Zgurovsky} et al., Evolution inclusions and variation inequalities for earth data processing. III. Long-time behavior of evolution inclusions solutions in earth data analysis. Berlin: Springer (2012; Zbl 1317.86003) Full Text: DOI
Kapustyan, O. V.; Kapustyan, O. A.; Sukretna, A. V. Approximate stabilization for a nonlinear parabolic boundary-value problem. (English. Russian original) Zbl 1235.35148 Ukr. Math. J. 63, No. 5, 759-767 (2011); translation from Ukr. Mat. Zh. 63, No. 5, 654-661 (2011). MSC: 35K20 35K58 35Q93 PDFBibTeX XMLCite \textit{O. V. Kapustyan} et al., Ukr. Math. J. 63, No. 5, 759--767 (2011; Zbl 1235.35148); translation from Ukr. Mat. Zh. 63, No. 5, 654--661 (2011) Full Text: DOI
Kapustyan, O. V.; Shklyar, T. B. On positive solutions of one class of evolutionary inclusions of the subdifferential type. (English. Russian original) Zbl 1242.49007 Ukr. Math. J. 63, No. 4, 544-554 (2011); translation from Ukr. Mat. Zh. 63, No. 4, 472-480 (2011). MSC: 49J15 49J52 PDFBibTeX XMLCite \textit{O. V. Kapustyan} and \textit{T. B. Shklyar}, Ukr. Math. J. 63, No. 4, 544--554 (2011; Zbl 1242.49007); translation from Ukr. Mat. Zh. 63, No. 4, 472--480 (2011) Full Text: DOI
Kapustyan, O. V.; Kasyanov, P. O.; Valero, J. Pullback attractors for a class of extremal solutions of the 3D Navier-Stokes system. (English) Zbl 1206.35048 J. Math. Anal. Appl. 373, No. 2, 535-547 (2011). Reviewer: Il’ya Sh. Mogilevskij (Tver’) MSC: 35B41 35Q35 49J20 35Q93 PDFBibTeX XMLCite \textit{O. V. Kapustyan} et al., J. Math. Anal. Appl. 373, No. 2, 535--547 (2011; Zbl 1206.35048) Full Text: DOI
Kapustyan, O.; Pankov, A. On the recurrence property of \(\omega\)-limit sets of multivalued semiflows. (Ukrainian. English summary) Zbl 1224.34154 Visn., Mat. Mekh., Kyïv. Univ. Im. Tarasa Shevchenka 2010, No. 23, 16-18 (2010). MSC: 34D05 37B20 47D99 PDFBibTeX XMLCite \textit{O. Kapustyan} and \textit{A. Pankov}, Visn., Mat. Mekh., Kyïv. Univ. Im. Tarasa Shevchenka 2010, No. 23, 16--18 (2010; Zbl 1224.34154)
Kapustyan, O. V.; Valero, J. Comparison between trajectory and global attractors for evolution systems without uniqueness of solutions. (English) Zbl 1202.37023 Int. J. Bifurcation Chaos Appl. Sci. Eng. 20, No. 9, 2723-2734 (2010). MSC: 37C70 47H20 35K57 35L90 PDFBibTeX XMLCite \textit{O. V. Kapustyan} and \textit{J. Valero}, Int. J. Bifurcation Chaos Appl. Sci. Eng. 20, No. 9, 2723--2734 (2010; Zbl 1202.37023) Full Text: DOI
Kapustyan, V. O.; Kogut, O. P. On the existence of optimal coefficient controls for a nonlinear Neumann boundary value problem. (English. Russian original) Zbl 1205.49005 Differ. Equ. 46, No. 7, 923-938 (2010); translation from Differ. Uravn. 46, No. 7, 915-930 (2010). MSC: 49J20 35Q93 35J40 PDFBibTeX XMLCite \textit{V. O. Kapustyan} and \textit{O. P. Kogut}, Differ. Equ. 46, No. 7, 923--938 (2010; Zbl 1205.49005); translation from Differ. Uravn. 46, No. 7, 915--930 (2010) Full Text: DOI
Kapustyan, O. V.; Kapustyan, O. A.; Sukretna, A. V. Approximate bounded synthesis for a weakly nonlinear boundary-value problem. (English. Ukrainian original) Zbl 1277.49006 Nonlinear Oscil., N.Y. 12, No. 3, 297-304 (2009); translation from Nelinijni Kolyvannya 12, No. 3, 291-298 (2009). MSC: 49J20 93B52 PDFBibTeX XMLCite \textit{O. V. Kapustyan} et al., Nonlinear Oscil., N.Y. 12, No. 3, 297--304 (2009; Zbl 1277.49006); translation from Nelinijni Kolyvannya 12, No. 3, 291--298 (2009) Full Text: DOI
Kapustyan, V. O.; Kohut, O. P. On the solvability of one class of problems of optimal control by coefficients in the principal part of a nonlinear elliptic operator. (English. Ukrainian original) Zbl 1277.35180 Nonlinear Oscil., N.Y. 12, No. 1, 60-73 (2009); translation from Nelinijni Kolyvannya 12, No. 1, 59-72 (2009). MSC: 35J62 49J20 PDFBibTeX XMLCite \textit{V. O. Kapustyan} and \textit{O. P. Kohut}, Nonlinear Oscil., N.Y. 12, No. 1, 60--73 (2009; Zbl 1277.35180); translation from Nelinijni Kolyvannya 12, No. 1, 59--72 (2009) Full Text: DOI
Kapustyan, O.; Shklyar, T. Qualitative behaviour of solutions of parabolic inclusion with translation-compact right-hand part. (Ukrainian. English summary) Zbl 1224.34198 Visn., Mat. Mekh., Kyïv. Univ. Im. Tarasa Shevchenka 2009, No. 22, 17-20 (2009). MSC: 34G25 34D45 PDFBibTeX XMLCite \textit{O. Kapustyan} and \textit{T. Shklyar}, Visn., Mat. Mekh., Kyïv. Univ. Im. Tarasa Shevchenka 2009, No. 22, 17--20 (2009; Zbl 1224.34198)
Kapustyan, A. V.; Valero, J. On the Kneser property for the complex Ginzburg-Landau equation and the Lotka-Volterra system with diffusion. (English) Zbl 1178.35077 J. Math. Anal. Appl. 357, No. 1, 254-272 (2009). Reviewer: Valerii V. Obukhovskij (Voronezh) MSC: 35B41 35K57 35B05 35Q35 92D25 35K51 PDFBibTeX XMLCite \textit{A. V. Kapustyan} and \textit{J. Valero}, J. Math. Anal. Appl. 357, No. 1, 254--272 (2009; Zbl 1178.35077) Full Text: DOI
Kapustyan, V. O.; Kas’yanov, P. O.; Kogut, O. P. On the solvability of one class of parameterized operator inclusions. (Ukrainian, English) Zbl 1199.47263 Ukr. Mat. Zh. 60, No. 12, 1619-1630 (2008); translation in Ukr. Math. J. 60, No. 12, 1901-1914 (2008). MSC: 47J22 PDFBibTeX XMLCite \textit{V. O. Kapustyan} et al., Ukr. Mat. Zh. 60, No. 12, 1619--1630 (2008; Zbl 1199.47263); translation in Ukr. Math. J. 60, No. 12, 1901--1914 (2008) Full Text: DOI
Kapustyan, Oleksij V.; Kapustyan, Olena A. Global attractor for impulsive-perturbed wave equation. (Ukrainian. English summary) Zbl 1199.37038 Visn., Ser. Fiz.-Mat. Nauky, Kyïv. Univ. Im. Tarasa Shevchenka 2008, No. 3, 69-74 (2008). MSC: 37C70 PDFBibTeX XMLCite \textit{O. V. Kapustyan} and \textit{O. A. Kapustyan}, Visn., Ser. Fiz.-Mat. Nauky, Kyïv. Univ. Im. Tarasa Shevchenka 2008, No. 3, 69--74 (2008; Zbl 1199.37038)
Iovane, G.; Kapustyan, A. V.; Valero, J. Asymptotic behaviour of reaction-diffusion equations with non-damped impulsive effects. (English) Zbl 1228.35063 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 68, No. 9, 2516-2530 (2008). MSC: 35B41 35B40 35K57 37B25 58C06 35R12 35K58 PDFBibTeX XMLCite \textit{G. Iovane} et al., Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 68, No. 9, 2516--2530 (2008; Zbl 1228.35063) Full Text: DOI
Kapustyan, O. V.; Melnik, V. S.; Valero, J. A weak attractor and properties of solutions for the three-dimensional Benard problem. (English) Zbl 1143.35013 Discrete Contin. Dyn. Syst. 18, No. 2-3, 449-481 (2007). Reviewer: A. Cichocka (Katowice) MSC: 35B41 35B40 35K55 35Q30 37B25 58C06 PDFBibTeX XMLCite \textit{O. V. Kapustyan} et al., Discrete Contin. Dyn. Syst. 18, No. 2--3, 449--481 (2007; Zbl 1143.35013) Full Text: DOI
Kapustyan, A. V.; Valero, J. Weak and strong attractors for the 3D Navier-Stokes system. (English) Zbl 1131.35056 J. Differ. Equations 240, No. 2, 249-278 (2007). Reviewer: Bruno Scarpellini (Basel) MSC: 35Q30 37L30 35B41 35K55 37B25 58C06 35B40 PDFBibTeX XMLCite \textit{A. V. Kapustyan} and \textit{J. Valero}, J. Differ. Equations 240, No. 2, 249--278 (2007; Zbl 1131.35056) Full Text: DOI
Kapustyan, Volodymyr O.; Kapustyan, Olena A.; Fartushnyj, Ivan D. Asymptotics of minimax estimates of functional from solutions of parabolic periodic boundary value problem in the class of bounded functions. (Ukrainian. English summary) Zbl 1142.35483 Visn., Ser. Fiz.-Mat. Nauky, Kyïv. Univ. Im. Tarasa Shevchenka 2006, No. 4, 166-171 (2006). MSC: 35K65 35B25 PDFBibTeX XMLCite \textit{V. O. Kapustyan} et al., Visn., Ser. Fiz.-Mat. Nauky, Kyïv. Univ. Im. Tarasa Shevchenka 2006, No. 4, 166--171 (2006; Zbl 1142.35483)
Kapustyan, O. Translation-compact distributions and minimal flows. (Ukrainian. English summary) Zbl 1120.35302 Visn., Mat. Mekh., Kyïv. Univ. Im. Tarasa Shevchenka 2006, No. 16, 72-75 (2006). MSC: 35B15 35D05 46F99 PDFBibTeX XMLCite \textit{O. Kapustyan}, Visn., Mat. Mekh., Kyïv. Univ. Im. Tarasa Shevchenka 2006, No. 16, 72--75 (2006; Zbl 1120.35302)
Valero, José; Kapustyan, Alexey On the connectedness and asymptotic behaviour of solutions of reaction-diffusion systems. (English) Zbl 1169.35345 J. Math. Anal. Appl. 323, No. 1, 614-633 (2006). MSC: 35K57 35K55 35B41 35K20 37L30 PDFBibTeX XMLCite \textit{J. Valero} and \textit{A. Kapustyan}, J. Math. Anal. Appl. 323, No. 1, 614--633 (2006; Zbl 1169.35345) Full Text: DOI
Kapustyan, O. V.; Valero, J.; Pereguda, O. V. Random attractor for the reaction-diffusion equation perturbed by a stochastic càdlàg process. (Ukrainian, English) Zbl 1114.37028 Teor. Jmovirn. Mat. Stat. 73, 52-62 (2005); translation in Theory Probab. Math. Stat., Vol 73, 57-69 (2006). Reviewer: Mikhail P. Moklyachuk (Kyïv) MSC: 37H10 34F05 60H10 37L30 PDFBibTeX XMLCite \textit{O. V. Kapustyan} et al., Teor. Ĭmovirn. Mat. Stat. 73, 52--62 (2005; Zbl 1114.37028); translation in Theory Probab. Math. Stat., Vol 73, 57--69 (2006) Full Text: Link
Iovane, G.; Kapustyan, O. V. Global attractor for impulsive reaction-diffusion equation. (English) Zbl 1108.35087 Nelinijni Kolyvannya 8, No. 3, 319-328 (2005). Reviewer: V. V. Vlasov (Moskva) MSC: 35K57 35R12 35B41 PDFBibTeX XMLCite \textit{G. Iovane} and \textit{O. V. Kapustyan}, Neliniĭni Kolyvannya 8, No. 3, 319--328 (2005; Zbl 1108.35087) Full Text: DOI Link
Kapustyan, O. V.; Pereguda, O. V.; Jose, V. Qualitative behavior of solutions for arbitrary perturbed reaction-diffusion equation. (Ukrainian) Zbl 1109.35363 Nelinijni Kolyvannya 8, No. 2, 174-185 (2005). Reviewer: R. K. Azimov (Andizhan) MSC: 35K57 60H15 PDFBibTeX XMLCite \textit{O. V. Kapustyan} et al., Neliniĭni Kolyvannya 8, No. 2, 174--185 (2005; Zbl 1109.35363) Full Text: DOI
Kapustyan, V. E.; Shamaev, E. V. Optimal control of the order of asymptotics for elliptic equations with fast oscillating coefficients. II: Substantiation of asymptotic expansions. (English. Russian original) Zbl 1118.49019 Cybern. Syst. Anal. 41, No. 3, 374-384 (2005); translation from Kibern. Sist. Anal. 2005, No. 3, 69-80 (2005). MSC: 49K20 49M30 PDFBibTeX XMLCite \textit{V. E. Kapustyan} and \textit{E. V. Shamaev}, Cybern. Syst. Anal. 41, No. 3, 374--384 (2005; Zbl 1118.49019); translation from Kibern. Sist. Anal. 2005, No. 3, 69--80 (2005) Full Text: DOI
Kapustyan, Volodymyr O.; Kapustyan, Olena A.; Podlipenko, Yuriĭ K. Minimax estimates of functional on time-periodic solutions of Neumann boundary value problems for parabolic equations. (Ukrainian. English summary) Zbl 1093.35502 Visn., Ser. Fiz.-Mat. Nauky, Kyïv. Univ. Im. Tarasa Shevchenka 2005, No. 2, 220-231 (2005). MSC: 35B10 35K20 PDFBibTeX XMLCite \textit{V. O. Kapustyan} et al., Visn., Ser. Fiz.-Mat. Nauky, Kyïv. Univ. Im. Tarasa Shevchenka 2005, No. 2, 220--231 (2005; Zbl 1093.35502)
Kapustyan, O. V. On existence of a minimal weakly attracting set in the phase space for 3D Navier-Stokes system. (Ukrainian. English summary) Zbl 1094.35093 Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 2005, No. 12, 18-22 (2005). MSC: 35Q30 37L30 PDFBibTeX XMLCite \textit{O. V. Kapustyan}, Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 2005, No. 12, 18--22 (2005; Zbl 1094.35093)