Shirikyan, Armen; Volevich, Leonid Qualitative properties of solutions for linear and nonlinear hyperbolic PDE’s. (English) Zbl 1053.35083 Discrete Contin. Dyn. Syst. 10, No. 1-2, 517-542 (2004). Reviewer: Messoud A. Efendiev (Berlin) MSC: 35L30 35L45 35L60 35L75 35B15 35B40 35B35 PDFBibTeX XMLCite \textit{A. Shirikyan} and \textit{L. Volevich}, Discrete Contin. Dyn. Syst. 10, No. 1--2, 517--542 (2004; Zbl 1053.35083) Full Text: DOI
Shirikyan, Armen; Volevich, Leonid Exponential dichotomy and time-bounded solutions for first-order hyperbolic systems. (English) Zbl 1017.35062 J. Dyn. Differ. Equations 14, No. 4, 777-827 (2002). Reviewer: Lutz Recke (Berlin) MSC: 35L45 34G10 47D06 34D09 PDFBibTeX XMLCite \textit{A. Shirikyan} and \textit{L. Volevich}, J. Dyn. Differ. Equations 14, No. 4, 777--827 (2002; Zbl 1017.35062) Full Text: DOI
Volevich, L. R.; Shirikyan, A. R. Stable and unstable manifolds for nonlinear elliptic equations with parameter. (English. Russian original) Zbl 0961.35056 Trans. Mosc. Math. Soc. 2000, 97-138 (2000); translation from Tr. Mosk. Mat. O.-va 61, 107-152 (2000). Reviewer: Mervan Pašić (Zagreb) MSC: 35J65 34G20 35B30 PDFBibTeX XMLCite \textit{L. R. Volevich} and \textit{A. R. Shirikyan}, Trans. Mosc. Math. Soc. 2000, 97--138 (2000; Zbl 0961.35056); translation from Tr. Mosk. Mat. O.-va 61, 107--152 (2000)
Volevich, L. R.; Shirikyan, A. R. Local dynamics for high-order semilinear hyperbolic equations. (English. Russian original) Zbl 0972.35074 Izv. Math. 64, No. 3, 439-485 (2000); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 64, No. 3, 3-50 (2000). Reviewer: Igor Andrianov (Köln) MSC: 35L75 37G05 35B20 35B40 35L30 37C15 PDFBibTeX XMLCite \textit{L. R. Volevich} and \textit{A. R. Shirikyan}, Izv. Math. 64, No. 3, 439--485 (2000; Zbl 0972.35074); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 64, No. 3, 3--50 (2000) Full Text: DOI
Shirikyan, A. R.; Volevich, L. R. A center manifold theorem for semilinear hyperbolic equations. (English) Zbl 0933.35142 ZAMM, Z. Angew. Math. Mech. 79, Suppl. 2, S313-S314 (1999). MSC: 35L75 37L10 35L30 PDFBibTeX XMLCite \textit{A. R. Shirikyan} and \textit{L. R. Volevich}, ZAMM, Z. Angew. Math. Mech. 79, S313--S314 (1999; Zbl 0933.35142)
Volevich, L. R.; Shirikyan, A. R. Stable and unstable manifolds for nonlinear elliptic equations with parameter. (English) Zbl 0933.35064 ZAMM, Z. Angew. Math. Mech. 79, Suppl. 3, S805-S806 (1999). MSC: 35J60 35B41 35B35 PDFBibTeX XMLCite \textit{L. R. Volevich} and \textit{A. R. Shirikyan}, ZAMM, Z. Angew. Math. Mech. 79, S805--S806 (1999; Zbl 0933.35064)
Shirikyan, Armen; Volevich, Leonid Asymptotic properties of solutions to high-order hyperbolic equations generalizing the damped wave equation. (English) Zbl 0929.35078 Fey, Michael (ed.) et al., Hyperbolic problems: Theory, numerics, applications. Proceedings of the 7th international conference, Zürich, Switzerland, February 1998. Vol. II. Basel: Birkhäuser. ISNM, Int. Ser. Numer. Math. 130, 885-894 (1999). Reviewer: Andrei Perjan (Chişinău) MSC: 35L25 35B40 35B15 PDFBibTeX XMLCite \textit{A. Shirikyan} and \textit{L. Volevich}, ISNM, Int. Ser. Numer. Math. 130, 885--894 (1999; Zbl 0929.35078)
Shirikyan, A.; Volevich, L. On infinite-dimensional dynamic systems generated by nonlinear hyperbolic equations. (English) Zbl 0918.58067 ZAMM, Z. Angew. Math. Mech. 78, Suppl. 3, S1073-S1074 (1998). Reviewer: Messoud Efendiev (Berlin) MSC: 35-XX PDFBibTeX XMLCite \textit{A. Shirikyan} and \textit{L. Volevich}, ZAMM, Z. Angew. Math. Mech. 78, S1073--S1074 (1998; Zbl 0918.58067) Full Text: DOI
Volevich, L. R.; Shirikyan, A. R. Exponential dichotomy and exponential splitting for hyperbolic equations. (English. Russian original) Zbl 0917.35069 Trans. Mosc. Math. Soc. 1998, 95-133 (1998); translation from Tr. Mosk. Mat. O.-va 59, 106-149 (1998). Reviewer: H.Tanabe (Toyonaka) MSC: 35L30 35B40 35B20 35L75 PDFBibTeX XMLCite \textit{L. R. Volevich} and \textit{A. R. Shirikyan}, Trans. Mosc. Math. Soc. 1998, 95--133 (1998; Zbl 0917.35069); translation from Tr. Mosk. Mat. O.-va 59, 106--149 (1998)
Shirikyan, Armen; Volevich, Leonid Bounded and almost periodic solutions of linear high-order hyperbolic equations. (English) Zbl 0912.35099 Math. Nachr. 193, 137-197 (1998). Reviewer: M.Reissig (Freiberg) MSC: 35L25 35B15 35B45 35A05 PDFBibTeX XMLCite \textit{A. Shirikyan} and \textit{L. Volevich}, Math. Nachr. 193, 137--197 (1998; Zbl 0912.35099) Full Text: DOI
Volevich, L. R.; Shirikyan, A. R. Bounded and almost periodic in time solutions of nonlinear hyperbolic equations of high order. (English. Russian original) Zbl 0892.35106 Trans. Mosc. Math. Soc. 1997, 89-135 (1997); translation from Tr. Mosk. Mat. O.-va. 58, 102-157 (1997). Reviewer: E.Feireisl (Praha) MSC: 35L75 35B15 35L30 PDFBibTeX XMLCite \textit{L. R. Volevich} and \textit{A. R. Shirikyan}, Trans. Mosc. Math. Soc. 1997, 89--135 (1997; Zbl 0892.35106); translation from Tr. Mosk. Mat. O.-va. 58, 102--157 (1997)
Shirikyan, Armen; Volevich, Leonid Linear high-order hyperbolic equations. Bounded and almost periodic in time solutions. (Équations linéaires hyperboliques d’ordre supérieur. Solutions bornées et presque-périodiques en temps.) (French. Abridged English version) Zbl 0879.35091 C. R. Acad. Sci., Paris, Sér. I 324, No. 8, 879-884 (1997). MSC: 35L25 35B15 PDFBibTeX XMLCite \textit{A. Shirikyan} and \textit{L. Volevich}, C. R. Acad. Sci., Paris, Sér. I 324, No. 8, 879--884 (1997; Zbl 0879.35091) Full Text: DOI
Volevich, Leonid R.; Shirikyan, Armen R. Quasilinear hyperbolic equations: Solutions bounded in time and almost periodic in time. (English) Zbl 0909.35096 Russ. J. Math. Phys. 4, No. 4, 527-538 (1996). MSC: 35L75 35B15 35B05 PDFBibTeX XMLCite \textit{L. R. Volevich} and \textit{A. R. Shirikyan}, Russ. J. Math. Phys. 4, No. 4, 527--538 (1996; Zbl 0909.35096)