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Regular attractors of semigroups and evolution equations. (English) Zbl 0565.47045

Let \(S=(S_ t)_{t\leq 0}\) be a strongly continuous semigroup of nonlinear operators on a Banach space E. In the paper sufficient conditions on S are given for the existence of a maximal attractor which can be represented as a finite union of instable manifolds. The abstract results are applied to nonlinear parabolic and hyperbolic equations.
Reviewer: M.Wolff

MSC:

47H20 Semigroups of nonlinear operators
58D07 Groups and semigroups of nonlinear operators
35K55 Nonlinear parabolic equations
35B35 Stability in context of PDEs
35B40 Asymptotic behavior of solutions to PDEs
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