On the damped semilinear wave equation with critical exponent
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.
scientific article; zbMATH DE number 2046202