Qualitative properties of solutions for linear and nonlinear hyperbolic PDE's
Armen Shirikyan - Laboratoire de Mathématiques, Université de Paris-Sud XI, Bâtiment 425, 91405 Orsay Cedex, France (email)
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.
Keywords: hyperbolic equations and systems; bounded and almost periodic solutions;exponential dichotomy; stable, unstable and center manifolds; linearization.
Received: July 2001; Revised: May 2002; Published: October 2003.
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