On the damped semilinear wave equation with critical exponent

Pages: 351 - 358, Issue Special, July 2003

 Abstract        Full Text (177.2K)              

Maurizio Grasselli - Dipartimento di Matematica, Politecnico di Milano, Via E. Bonardi, 9, I-20133 Milano, Italy (email)
Vittorino Pata - Politecnico di Milano - Dipartimento di Matematica "F. Brioschi", Via Bonardi 9, 20133 Milano, Italy (email)

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.

Keywords:  Damped wave equation, universal attractors, upper semicontinuity, exponential attractors.
Mathematics Subject Classification:  Primary: 35B41, 35L05; Secondary: 35L25, 35Q40.

Received: June 2002;      Revised: March 2003;      Published: April 2003.