Communications on Pure and Applied Analysis (CPAA)

Weakly dissipative semilinear equations of viscoelasticity

Pages: 705 - 720, Volume 4, Issue 4, December 2005      doi:10.3934/cpaa.2005.4.705

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Monica Conti - Dipartimento di Matematica "F.Brioschi", Politecnico di Milano, I-20133 Milano, Italy (email)
V. Pata - Dipartimento di Matematica "F. Brioschi", Politecnico di Milano, I-20133 Milano, Italy (email)

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.

Keywords:  Hyperbolic equations with memory, dynamical systems, Lyapunov functionals, gradient systems, global attractors
Mathematics Subject Classification:  35B40, 35L70, 37L45, 45K05, 74D99

Received: December 2004;      Revised: March 2005;      Available Online: September 2005.