Upper semicontinuity of attractors for approximations of semigroups and partial differential equations

Authors:
Jack K. Hale, Xiao-Biao Lin and GeneviÃ¨ve Raugel

Journal:
Math. Comp. **50** (1988), 89-123

MSC:
Primary 47H20; Secondary 35K55, 35K70, 65N30

DOI:
https://doi.org/10.1090/S0025-5718-1988-0917820-X

MathSciNet review:
917820

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Abstract | References | Similar Articles | Additional Information

Abstract: Suppose a given evolutionary equation has a compact attractor and the evolutionary equation is approximated by a finite-dimensional system. Conditions are given to ensure the approximate system has a compact attractor which converges to the original one as the approximation is refined. Applications are given to parabolic and hyperbolic partial differential equations.

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DOI:
https://doi.org/10.1090/S0025-5718-1988-0917820-X

Article copyright:
© Copyright 1988
American Mathematical Society