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2003, 2003(Special): 351-358. doi: 10.3934/proc.2003.2003.351

On the damped semilinear wave equation with critical exponent

Maurizio Grasselli 1, and  Vittorino Pata 2,

1. 

Dipartimento di Matematica, Politecnico di Milano, Via E. Bonardi, 9, I-20133 Milano, Italy
2. 

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

Received  June 2002 Revised  March 2003 Published  April 2003

We provide an optimal regularity result for the universal attractor of the weakly damped semilinear wave equation, when the nonlinearity satisfies the critical growth condition. This allows us to prove an upper semicontinuity result as well as the existence of an exponential attractor.
Keywords: exponential attractors., upper semicontinuity, Damped wave equation, universal attractors.
Mathematics Subject Classification: Primary: 35B41, 35L05; Secondary: 35L25, 35Q4.
Citation: Maurizio Grasselli, Vittorino Pata. On the damped semilinear wave equation with critical exponent. Conference Publications, 2003, 2003 (Special) : 351-358. doi: 10.3934/proc.2003.2003.351
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