November  2010, 27(4): 1535-1552. doi: 10.3934/dcds.2010.27.1535

Semilinear wave equations of viscoelasticity in the minimal state framework

1. 

Politecnico di Milano - Dipartimento di Matematica "F. Brioschi", Via Bonardi 9, 20133 Milano

2. 

Politecnico di Milano - Dipartimento di Matematica “F. Brioschi”, Via Bonardi 9, 20133 Milano, Italy

Received  September 2009 Revised  November 2009 Published  March 2010

A semilinear integrodifferential equation of hyperbolic type is studied, where the dissipation is entirely contributed by the convolution term accounting for the past history of the variable. Within a novel abstract framework, based on the notion of minimal state, the existence of a regular global attractor is proved.
Citation: Monica Conti, Elsa M. Marchini, Vittorino Pata. Semilinear wave equations of viscoelasticity in the minimal state framework. Discrete and Continuous Dynamical Systems, 2010, 27 (4) : 1535-1552. doi: 10.3934/dcds.2010.27.1535
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