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Weak attractor for damped abstract nonlinear hyperbolic systems. (English) Zbl 0911.35020

The paper is a continuation of the investigations of the work of H. T. Banks, D. S. Gilliam and V. I. Shubov [Differ. Integral Equ. 10, 309-332 (1997; Zbl 0892.47063)], in which the existence and uniqueness of weak solutions for damped abstract nonlinear hyperbolic systems were established. Under an additional assumption, the author proves the existence of a weak dynamical system, a weak compact global attractor, the existence of a global Lyapunov function and makes same statements concerning the asymptotic behaviour of the solutions. This class of nonlinear systems arises as a dynamical model for elastomers.

MSC:

35B40 Asymptotic behavior of solutions to PDEs
35L60 First-order nonlinear hyperbolic equations
35G25 Initial value problems for nonlinear higher-order PDEs

Citations:

Zbl 0892.47063