On the damped semilinear wave equation with critical exponent
type: Item
instance of: scholarly article
title: On the damped semilinear wave equation with critical exponent
zbMATH Open document ID: 1058.35044
author: Maurizio Grasselli
author: Vittorino Pata
published in: Discrete and Continuous Dynamical Systems
publication date: 2004-02-23T00:00:00Z
review text: The paper gives an optimal regularity results for the universal attractor of the semigroup to the equation \(\mu u_{tt}+u_{t}-\triangle u+f(u)=g\) (\(t>0,x\in \Omega \subset \mathbb{R}^3\)) and Dirichlet boundary condition, where \(\mu \) is a small parameter, \(g=g(x)\) and \(f(u)\) satisfies critical growth conditions. An upper semicontinuity result for \(\mu \rightarrow 0\) and the existence of an exponential attractor are proved.
Mathematics Subject Classification ID: 35B41
Mathematics Subject Classification ID: 35L70
Mathematics Subject Classification ID: 35L20
Mathematics Subject Classification ID: 35B25
Mathematics Subject Classification ID: 35B33
zbMATH DE Number: 2046202
zbMATH Keywords: damped wave equation
zbMATH Keywords: initial boundary value problem
zbMATH Keywords: attractor
zbMATH Keywords: critical exponent
zbMATH Keywords: optimal regularity results
zbMATH Keywords: Dirichlet boundary condition
zbMATH Keywords: critical growth conditions
reviewed by: Marie Kopáčková
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2046202