Lower semicontinuity of attractors of gradient systems and applications |
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Authors: | Jack K Hale Geneviève Raugel |
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Institution: | (1) Present address: School of Mathematics, Georgia Institute of Technology, 30332 Atlanta, GA, USA;(2) Present address: Unité de Recherche Associée au CNRS-756, École Polytechnique, Centre de Mathématiques Appliquées, 91128 Palaiseau Cedex, France |
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Abstract: | Summary For 00, let T(t), t0, be a family of semigroups on a Banach space X with local attractors A. Under the assumptions that T0(t) is a gradient system with hyperbolic equilibria and T(t) converges to T0(t) in an appropriate sense, it is shown that the attractors {A, 00} are lower-semicontinuous at zero. Applications are given to ordinary and functional differential equations, parabolic partial differential equations and their space and time discretizations. We also give an estimate of the Hausdorff distance between A and A0, in some examples.Research supported by U.S. Army Research Office DAAL-03-86-K-0074 and the National Science Foundation DMS-8507056. |
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