Existence of a Global Attractor for Semilinear Dissipative Wave Equations on RN

Abstract

We consider the semilinear hyperbolic problem, with the initial conditions u(x, 0)=u 0 (x) and u t (x, 0)=u 1 (x) in the case where N 3 and (,(x))is introduced, to overcome the difficulties related with the noncompactness of operators which arise in unbounded domains. We derive various estimates to show local existence of solutions and existence of a global attractor in X 0 . The compactness of the embedding) is widely applied.1999 Academic Press

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