Kusaba, Ryunosuke; Ozawa, Tohru Weighted estimates and large time behavior of small amplitude solutions to the semilinear heat equation. (English) Zbl 07812189 Differ. Equ. Appl. 15, No. 3, 235-268 (2023). MSC: 35K91 35B40 35C20 PDFBibTeX XMLCite \textit{R. Kusaba} and \textit{T. Ozawa}, Differ. Equ. Appl. 15, No. 3, 235--268 (2023; Zbl 07812189) Full Text: DOI arXiv
Miyake, Nobuhito Effect of decay rates of initial data on the sign of solutions to Cauchy problems of polyharmonic heat equations. (English) Zbl 1522.35303 Math. Ann. 387, No. 1-2, 265-289 (2023). MSC: 35K30 35B05 35B09 35K58 PDFBibTeX XMLCite \textit{N. Miyake}, Math. Ann. 387, No. 1--2, 265--289 (2023; Zbl 1522.35303) Full Text: DOI
Fila, Marek; Ishige, Kazuhiro; Kawakami, Tatsuki Solvability of the heat equation on a half-space with a dynamical boundary condition and unbounded initial data. (English) Zbl 1518.35425 Z. Angew. Math. Phys. 74, No. 4, Paper No. 143, 17 p. (2023). MSC: 35K05 35K20 35A01 PDFBibTeX XMLCite \textit{M. Fila} et al., Z. Angew. Math. Phys. 74, No. 4, Paper No. 143, 17 p. (2023; Zbl 1518.35425) Full Text: DOI arXiv
Eom, Junyong Large time behavior of ODE type solutions to higher-order semilinear parabolic equations with small initial data. (English) Zbl 1498.35071 J. Math. Anal. Appl. 517, No. 2, Article ID 126625, 15 p. (2023). MSC: 35B40 35K30 35K58 PDFBibTeX XMLCite \textit{J. Eom}, J. Math. Anal. Appl. 517, No. 2, Article ID 126625, 15 p. (2023; Zbl 1498.35071) Full Text: DOI
Ishige, Kazuhiro; Kawakami, Tatsuki; Okabe, Shinya Existence of solutions to nonlinear parabolic equations via majorant integral kernel. (English) Zbl 1495.35096 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 223, Article ID 113025, 22 p. (2022). MSC: 35K30 35K08 35K58 35R11 45G10 PDFBibTeX XMLCite \textit{K. Ishige} et al., Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 223, Article ID 113025, 22 p. (2022; Zbl 1495.35096) Full Text: DOI arXiv
Penent, Guillaume; Privault, Nicolas Existence and probabilistic representation of the solutions of semilinear parabolic PDEs with fractional Laplacians. (English) Zbl 1495.35104 Stoch. Partial Differ. Equ., Anal. Comput. 10, No. 2, 446-474 (2022). MSC: 35K58 35B65 35R11 47G30 35S05 35S10 60J85 65R20 60G51 60G52 65C05 45D05 33C05 60H07 PDFBibTeX XMLCite \textit{G. Penent} and \textit{N. Privault}, Stoch. Partial Differ. Equ., Anal. Comput. 10, No. 2, 446--474 (2022; Zbl 1495.35104) Full Text: DOI arXiv
Furioli, Giulia; Kawakami, Tatsuki; Terraneo, Elide Heat equation with an exponential nonlinear boundary condition in the half space. (English) Zbl 1490.35206 SN Partial Differ. Equ. Appl. 3, No. 3, Paper No. 36, 44 p. (2022). MSC: 35K60 35A01 35B40 46E30 PDFBibTeX XMLCite \textit{G. Furioli} et al., SN Partial Differ. Equ. Appl. 3, No. 3, Paper No. 36, 44 p. (2022; Zbl 1490.35206) Full Text: DOI
Fujishima, Yohei; Ioku, Norisuke Solvability of a semilinear heat equation via a quasi scale invariance. (English) Zbl 1473.35341 Ferone, Vincenzo (ed.) et al., Geometric properties for parabolic and elliptic PDE’s. Contributions of the 6th Italian-Japanese workshop, Cortona, Italy, May 20–24, 2019. Cham: Springer. Springer INdAM Ser. 47, 79-101 (2021). MSC: 35K58 35K15 PDFBibTeX XMLCite \textit{Y. Fujishima} and \textit{N. Ioku}, Springer INdAM Ser. 47, 79--101 (2021; Zbl 1473.35341) Full Text: DOI
Braga, Gastão A.; Moreira, Jussara M.; Souza, Camila F. Asymptotics for nonlinear integral equations with a generalized heat kernel using renormalization group technique. II: Marginal perturbations and logarithmic corrections to the time decay of solutions. (English) Zbl 1475.45018 J. Math. Phys. 62, No. 8, Article ID 083507, 12 p. (2021). Reviewer: Vincenzo Vespri (Firenze) MSC: 45M05 45G10 35K08 PDFBibTeX XMLCite \textit{G. A. Braga} et al., J. Math. Phys. 62, No. 8, Article ID 083507, 12 p. (2021; Zbl 1475.45018) Full Text: DOI arXiv
Otsmane, Sarah Asymptotically self-similar global solutions for a complex-valued quadratic heat equation with a generalized kernel. (English) Zbl 1470.35108 Bol. Soc. Mat. Mex., III. Ser. 27, No. 2, Paper No. 46, 53 p. (2021). MSC: 35C06 35B40 35K08 35K45 35K58 35K65 PDFBibTeX XMLCite \textit{S. Otsmane}, Bol. Soc. Mat. Mex., III. Ser. 27, No. 2, Paper No. 46, 53 p. (2021; Zbl 1470.35108) Full Text: DOI
Fila, Marek; Ishige, Kazuhiro; Kawakami, Tatsuki The large diffusion limit for the heat equation with a dynamical boundary condition. (English) Zbl 1450.35031 Commun. Contemp. Math. 23, No. 1, Article ID 2050003, 20 p. (2021). MSC: 35B25 35K05 35A01 35K20 35B30 PDFBibTeX XMLCite \textit{M. Fila} et al., Commun. Contemp. Math. 23, No. 1, Article ID 2050003, 20 p. (2021; Zbl 1450.35031) Full Text: DOI arXiv
Grunau, Hans-Christoph; Miyake, Nobuhito; Okabe, Shinya Positivity of solutions to the Cauchy problem for linear and semilinear biharmonic heat equations. (English) Zbl 1447.35179 Adv. Nonlinear Anal. 10, 353-370 (2021). MSC: 35K30 35B09 35K58 PDFBibTeX XMLCite \textit{H.-C. Grunau} et al., Adv. Nonlinear Anal. 10, 353--370 (2021; Zbl 1447.35179) Full Text: DOI arXiv
Ishige, Kazuhiro; Kawakami, Tatsuki; Okabe, Shinya Existence of solutions for a higher-order semilinear parabolic equation with singular initial data. (English) Zbl 1454.35222 Ann. Inst. Henri Poincaré, Anal. Non Linéaire 37, No. 5, 1185-1209 (2020). MSC: 35K58 35K30 PDFBibTeX XMLCite \textit{K. Ishige} et al., Ann. Inst. Henri Poincaré, Anal. Non Linéaire 37, No. 5, 1185--1209 (2020; Zbl 1454.35222) Full Text: DOI arXiv
Ishige, Kazuhiro; Miyake, Nobuhito; Okabe, Shinya Blowup for a fourth-order parabolic equation with gradient nonlinearity. (English) Zbl 1431.35057 SIAM J. Math. Anal. 52, No. 1, 927-953 (2020). MSC: 35K25 35K55 35B44 35Q74 74H20 74K35 PDFBibTeX XMLCite \textit{K. Ishige} et al., SIAM J. Math. Anal. 52, No. 1, 927--953 (2020; Zbl 1431.35057) Full Text: DOI
Fujishima, Yohei; Kawakami, Tatsuki; Sire, Yannick Critical exponent for the global existence of solutions to a semilinear heat equation with degenerate coefficients. (English) Zbl 1419.35122 Calc. Var. Partial Differ. Equ. 58, No. 2, Paper No. 62, 25 p. (2019). Reviewer: Fatma Gamze Duzgun (Ankara) MSC: 35K58 35B33 35K65 PDFBibTeX XMLCite \textit{Y. Fujishima} et al., Calc. Var. Partial Differ. Equ. 58, No. 2, Paper No. 62, 25 p. (2019; Zbl 1419.35122) Full Text: DOI
Braga, Gastão A.; Moreira, Jussara M.; Souza, Camila F. Asymptotics for nonlinear integral equations with a generalized heat kernel using renormalization group technique. (English) Zbl 1408.45002 J. Math. Phys. 60, No. 1, 013507, 13 p. (2019). Reviewer: Andrey Zahariev (Plovdiv) MSC: 45G10 45M05 35K08 81T17 PDFBibTeX XMLCite \textit{G. A. Braga} et al., J. Math. Phys. 60, No. 1, 013507, 13 p. (2019; Zbl 1408.45002) Full Text: DOI
Hisa, Kotaro; Ishige, Kazuhiro Existence of solutions for a fractional semilinear parabolic equation with singular initial data. (English) Zbl 1393.35275 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 175, 108-132 (2018). MSC: 35R11 PDFBibTeX XMLCite \textit{K. Hisa} and \textit{K. Ishige}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 175, 108--132 (2018; Zbl 1393.35275) Full Text: DOI arXiv
Ishige, Kazuhiro; Kawakami, Tatsuki; Michihisa, Hironori Asymptotic expansions of solutions of fractional diffusion equations. (English) Zbl 1372.35338 SIAM J. Math. Anal. 49, No. 3, 2167-2190 (2017). MSC: 35R11 35C20 35K58 35B44 PDFBibTeX XMLCite \textit{K. Ishige} et al., SIAM J. Math. Anal. 49, No. 3, 2167--2190 (2017; Zbl 1372.35338) Full Text: DOI arXiv
Furioli, Giulia; Kawakami, Tatsuki; Ruf, Bernhard; Terraneo, Elide Asymptotic behavior and decay estimates of the solutions for a nonlinear parabolic equation with exponential nonlinearity. (English) Zbl 1361.35069 J. Differ. Equations 262, No. 1, 145-180 (2017). Reviewer: Lubomira Softova (Aversa) MSC: 35K20 35K58 PDFBibTeX XMLCite \textit{G. Furioli} et al., J. Differ. Equations 262, No. 1, 145--180 (2017; Zbl 1361.35069) Full Text: DOI arXiv
Fila, Marek; Ishige, Kazuhiro; Kawakami, Tatsuki Positive solutions of a semilinear elliptic equation with singular Dirichlet boundary data. (English) Zbl 1386.35099 J. Elliptic Parabol. Equ. 1, No. 2, 335-362 (2015). MSC: 35J61 35B40 35J25 PDFBibTeX XMLCite \textit{M. Fila} et al., J. Elliptic Parabol. Equ. 1, No. 2, 335--362 (2015; Zbl 1386.35099) Full Text: DOI
Ishige, Kazuhiro; Kawakami, Tatsuki; Kobayashi, Kanako Asymptotics for a nonlinear integral equation with a generalized heat kernel. (English) Zbl 1333.45010 J. Evol. Equ. 14, No. 4-5, 749-777 (2014). Reviewer: Martin Väth (Prague) MSC: 45M05 35K08 45G10 35K05 35C15 35R11 35K58 PDFBibTeX XMLCite \textit{K. Ishige} et al., J. Evol. Equ. 14, No. 4--5, 749--777 (2014; Zbl 1333.45010) Full Text: DOI arXiv