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

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

doi:10.1090/S0025-5718-1988-0917820-X

Upper semicontinuity of attractors for approximations of semigroups and partial differential equations
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by Jack K. Hale, Xiao-Biao Lin and Geneviève Raugel PDF

Math. Comp. 50 (1988), 89-123 Request permission

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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