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Upper semicontinuity of attractors for approximations of semigroups and partial differential equations. (English) Zbl 0666.35013

The authors suppose that a given evolutionary equation has a compact attractor and that the evolutionary equation is approximated by a finite dimensional systems. The authors give conditions to insure that the approximation equation (system) has a compact attractor which converges to the original attractor, as the approximation scheme is refined. They illustrate how this methodology applied to both hyperbolic and parabolic partial differential equations.
Reviewer: M.Witten

MSC:

35B40 Asymptotic behavior of solutions to PDEs
65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
65N99 Numerical methods for partial differential equations, boundary value problems
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
37C70 Attractors and repellers of smooth dynamical systems and their topological structure
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