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

Filippo Dell'Oro

doi:10.3934/cpaa.2013.12.1015

Article Contents

2013, Volume 12, Issue 2: 1015-1027. Doi: 10.3934/cpaa.2013.12.1015

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

Filippo Dell'Oro^1,

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

Received: July 31, 2011

Revised: February 29, 2012

Published: February 2013

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Abstract

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.

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Mathematics Subject Classification: Primary: 35B33, 35B40, 35L05; Secondary: 35M10.

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