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March  2013, 12(2): 1015-1027. doi: 10.3934/cpaa.2013.12.1015

Global attractors for strongly damped wave equations with subcritical-critical nonlinearities

 1 Dipartimento di Matematica "Francesco Brioschi", Politecnico di Milano, Via Bonardi 9, Milano 20133, Italy

Received  August 2011 Revised  March 2012 Published  September 2012

This paper is concerned with the nonlinear strongly damped wave equation \begin{eqnarray*} u_{t t}-\Delta u_t-\Delta u+f(u_t)+g(u)=h, \end{eqnarray*} with Dirichlet boundary conditions and a time-independent external force $h$. In the presence of nonlinearities $f$ and $g$ of subcritical and critical growth, respectively, the existence of a global attractor of optimal regularity is established.
Citation: Filippo Dell'Oro. Global attractors for strongly damped wave equations with subcritical-critical nonlinearities. Communications on Pure & Applied Analysis, 2013, 12 (2) : 1015-1027. doi: 10.3934/cpaa.2013.12.1015
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