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Mathematics of Computation

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

Authors: Jack K. Hale, Xiao-Biao Lin and Geneviève Raugel
Journal: Math. Comp. 50 (1988), 89-123
MSC: Primary 47H20; Secondary 35K55, 35K70, 65N30
MathSciNet review: 917820
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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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Article copyright: © Copyright 1988 American Mathematical Society