December  2005, 4(4): 705-720. doi: 10.3934/cpaa.2005.4.705

Weakly dissipative semilinear equations of viscoelasticity

1. 

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

Received  December 2004 Revised  March 2005 Published  September 2005

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.
Citation: Monica Conti, V. Pata. Weakly dissipative semilinear equations of viscoelasticity. Communications on Pure & Applied Analysis, 2005, 4 (4) : 705-720. doi: 10.3934/cpaa.2005.4.705
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