Global attractor for damped abstract nonlinear hyperbolic systems

This work is concerned with the long time dynamics of a class of abstract nonlinear second order in time systems with damping. This class of systems describes nonlinear dissipative elastic models with the nonlinear term produced by neo-Hookean type stress–strain relationships. In the present work, w...

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Bibliographic Details
Published in:Nonlinear analysis 2003-05, Vol.53 (5), p.653-668
Main Author: PINTER, Gabriella A
Format: Article
Language:English
Subjects:
Dynamical system
Exact sciences and technology
Global analysis, analysis on manifolds
Global attractor
Lyapunov function
Mathematical analysis
Mathematics
Partial differential equations
Sciences and techniques of general use
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
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Summary:This work is concerned with the long time dynamics of a class of abstract nonlinear second order in time systems with damping. This class of systems describes nonlinear dissipative elastic models with the nonlinear term produced by neo-Hookean type stress–strain relationships. In the present work, we use an analysis based in part on the results of H.T. Banks, D.S. Gilliam and V.I. Shubov on the existence and uniqueness of the weak solutions to show that these systems generate a “strong” dynamical system also. More importantly, we are able to prove the existence of a compact “strong” global attractor. Finally, we make several comments concerning the regularity of this attractor, and present some examples.
ISSN:0362-546X
1873-5215
DOI:10.1016/S0362-546X(02)00264-X