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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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\textit{J. K. Hale} et al., Math. Comput. 50, No. 181, 89--123 (1988; Zbl 0666.35013)

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### References:

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