We prove the existence of the universal attractor for the strongly damped semilinear wave equation, in 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.

On the strongly damped wave equation

PATA, VITTORINO;
2005-01-01

Abstract

We prove the existence of the universal attractor for the strongly damped semilinear wave equation, in 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.
2005
File in questo prodotto:
File Dimensione Formato  
PS.pdf

Accesso riservato

: Post-Print (DRAFT o Author’s Accepted Manuscript-AAM)
Dimensione 227.73 kB
Formato Adobe PDF
227.73 kB Adobe PDF   Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/555099
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 124
  • ???jsp.display-item.citation.isi??? 115
social impact