Finite-dimensional attractors for a general class of nonautonomous wave equations
The authors deal with a large-time asymptotic of a general nonautonomous wave equation of the form \[ Pu''+ Qu'+ Au+ F(t, u)= h(t) \] in a Hilbert space \(H\), where \(A\), \(P\), and \(Q\) are linear positive selfadjoint operators. Under some general conditions the authors prove the existence of an exponential attractor and as a consequence obtain a global finite-dimensional attractor. To this end they use that the corresponding ``semigroup'' \(S(t)\) is an \(\alpha\)-contraction and verify the squeezing property.
scientific article; zbMATH DE number 1531170