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

Hale, Jack K.; Lin, Xiao-Biao; Raugel, Geneviève

Math. Comput. 50, No. 181, 89-123 (1988).

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

Keywords:

evolutionary equation; compact attractor; approximation

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