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

Armen Shirikyan; Leonid Volevich

doi:10.3934/dcds.2004.10.517

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2004, Volume 10, Issue 1&2: 517-542. Doi: 10.3934/dcds.2004.10.517

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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
2.
Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, 4 Miusskaya Square, 125047 Moscow

Received: July 2001

Revised: May 2002

Published: January 2004

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Abstract

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.

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Mathematics Subject Classification: 35L25, 35L40, 35L60, 35L75, 35B15, 35B40.

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