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On the damped semilinear wave equation with critical exponent. (English) Zbl 1058.35044

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.

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
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