Grasselli, Maurizio; Pata, Vittorino On the damped semilinear wave equation with critical exponent. (English) Zbl 1058.35044 Discrete Contin. Dyn. Syst. 2003, Suppl. Vol., 351-358 (2003). 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. Reviewer: Marie Kopáčková (Praha) Cited in 13 Documents MSC: 35B41 Attractors 35L70 Second-order nonlinear hyperbolic equations 35L20 Initial-boundary value problems for second-order hyperbolic equations 35B25 Singular perturbations in context of PDEs 35B33 Critical exponents in context of PDEs Keywords:damped wave equation; initial boundary value problem; attractor; critical exponent; optimal regularity results; Dirichlet boundary condition; critical growth conditions PDFBibTeX XMLCite \textit{M. Grasselli} and \textit{V. Pata}, Discrete Contin. Dyn. Syst. 2003, 351--358 (2003; Zbl 1058.35044)