Reduction of Infinite Dimensional Systems to Finite Dimensions: Compact Convergence Approach

We consider parameter dependent semilinear evolution problems for which, at the limit value of the parameter, the problem is finite dimensional. We introduce an abstract functional analytic framework that applies to many problems in the existing literature for which the study of asymptotic dynamics...

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Bibliographic Details
Published inSIAM journal on mathematical analysis Vol. 45; no. 2; pp. 600 - 638
Main Authors Carvalho, A. N., Cholewa, J. W., Lozada-Cruz, G., Primo, M. R. T.
Format Journal Article
LanguageEnglish
Published Philadelphia Society for Industrial and Applied Mathematics 01.01.2013
Subjects
Asymptotic properties
Banach spaces
Convergence
Dynamic tests
Eigenvalues
Evolution
Homogenization
Invariants
Manifolds
Mathematical analysis
Mathematical models
Neurosciences
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Summary:We consider parameter dependent semilinear evolution problems for which, at the limit value of the parameter, the problem is finite dimensional. We introduce an abstract functional analytic framework that applies to many problems in the existing literature for which the study of asymptotic dynamics can be reduced to finite dimensions via the invariant manifolds technique. Some practical models are considered to show wide applicability of the theory. [PUBLICATION ABSTRACT]
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ISSN:0036-1410
1095-7154
DOI:10.1137/10080734X