On the strongly damped wave equation

Vittorino Pata, Marco Squassina

Research output: Contribution to journalArticlepeer-review

99 Citations (Scopus)


We prove the existence of the universal attractor for the strongly damped semilinear wave equation, in the presence of a quite general nonlinearity of critical growth. When the nonlinearity is subcritical, we prove the existence of an exponential attractor of optimal regularity, having a basin of attraction coinciding with the whole phase-space. As a byproduct, the universal attractor is regular and of finite fractal dimension. Moreover, we carry out a detailed analysis of the asymptotic behavior of the solutions in dependence of the damping coefficient.
Original languageEnglish
Pages (from-to)511-533
Number of pages23
JournalCommunications in Mathematical Physics
Publication statusPublished - 2005


  • Strongly damped wave equations


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