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Discrete and Continuous Dynamical Systems - Series A (DCDS-A)
 

Semilinear wave equations of viscoelasticity in the minimal state framework

Pages: 1535 - 1552, Volume 27, Issue 4, August 2010      doi:10.3934/dcds.2010.27.1535

 
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Monica Conti - Politecnico di Milano - Dipartimento di Matematica "F. Brioschi", Via Bonardi 9, 20133 Milano, Italy (email)
Elsa M. Marchini - Politecnico di Milano - Dipartimento di Matematica “F. Brioschi”, Via Bonardi 9, 20133 Milano, Italy (email)
Vittorino Pata - Politecnico di Milano - Dipartimento di Matematica "F. Brioschi", Via Bonardi 9, 20133 Milano, Italy (email)

Abstract: 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.

Keywords:  Hyperbolic equation with memory, viscoelasticity, minimal state, global attractor.
Mathematics Subject Classification:  Primary: 35B40, 35L70; Secondary: 37L45, 45K05, 74D99.

Received: September 2009;      Revised: November 2009;      Available Online: March 2010.