Qualitative properties of solutions for linear and nonlinear hyperbolic PDE's

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January & February 2004, 10(1&2): 517-542. doi: 10.3934/dcds.2004.10.517

Qualitative properties of solutions for linear and nonlinear hyperbolic PDE's

Armen Shirikyan ^1, and Leonid Volevich ^2,

1.	Laboratoire de Mathématiques, Université de Paris-Sud XI, Bâtiment 425, 91405 Orsay Cedex, France
2.	Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, 4 Miusskaya Square, 125047 Moscow, Russian Federation

Received July 2001 Revised May 2002 Published October 2003

Abstract
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We present a number of results concerning large-time qualitative behavior of solutions for high-order hyperbolic equations and first-order hyperbolic systems. We discuss the properties of exponential stability and exponential dichotomy, construction of stable, unstable, and center manifolds, Grobman--Hartman type theorems on linearization of the phase portrait, and existence and uniqueness of time-bounded and almost periodic (AP) solutions.

Keywords: unstable and center manifolds; linearization., hyperbolic equations and systems; bounded and almost periodic solutions;exponential dichotomy; stable.

Mathematics Subject Classification: 35L25, 35L40, 35L60, 35L75, 35B15, 35B4.

Citation: Armen Shirikyan, Leonid Volevich. Qualitative properties of solutions for linear and nonlinear hyperbolic PDE's. Discrete & Continuous Dynamical Systems - A, 2004, 10 (1&2) : 517-542. doi: 10.3934/dcds.2004.10.517

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