On the damped semilinear wave equation with critical exponent

Maurizio Grasselli; Vittorino Pata

doi:10.3934/proc.2003.2003.351

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2003, Volume 2003: 351-358. Doi: 10.3934/proc.2003.2003.351 open access

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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
2.
Politecnico di Milano - Dipartimento di Matematica "F. Brioschi", Via Bonardi 9, 20133 Milano

Received: May 31, 2002

Revised: February 28, 2003

Published: March 2003

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Abstract

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.

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Mathematics Subject Classification: Primary: 35B41, 35L05; Secondary: 35L25, 35Q40.

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