Weakly dissipative semilinear equations of viscoelasticity

Monica Conti; V. Pata

doi:10.3934/cpaa.2005.4.705

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2005, Volume 4, Issue 4: 705-720. Doi: 10.3934/cpaa.2005.4.705

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Weakly dissipative semilinear equations of viscoelasticity

Monica Conti^1, and
V. Pata^1,

1.
Dipartimento di Matematica "F.Brioschi", Politecnico di Milano, I-20133 Milano

Received: November 30, 2004

Revised: February 28, 2005

Published: November 2005

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Abstract

We consider an integro-partial differential equation of hyperbolic type with a cubic nonlinearity, in which no dissipation mechanism is present, except for the convolution term accounting for the past memory of the variable. Setting the equation in the history space framework, we prove the existence of a regular global attractor.

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Mathematics Subject Classification: 35B40, 35L70, 37L45, 45K05, 74D99.

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