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Reduction of dimension of approximate intertial manifolds by symmetry

Published online by Cambridge University Press:  17 April 2009

Anibal Rodriguez-Bernal  and
Bixiang Wang
Anibal Rodriguez-Bernal
Affiliation:
Departmento de Matematica Aplicada, Universidad Complutense de Madrid, Madrid 28040, Spain
Bixiang Wang
Affiliation:
Departmento de Matematica Aplicada, Universidad Complutense de Madrid, Madrid 28040, Spain and Department of Applied Mathematics, Tsinghua University, Beijing 100084, China
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In this paper, we study approximate inertial manifolds for nonlinear evolution partial differential equations which possess symmetry. The relationship between symmetry and dimensions of approximate inertial manifolds is established. We demonstrate that symmetry can reduce the dimensions of an approximate inertial manifold. Applications for concrete evolution equations are given.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 60 , Issue 2 , October 1999 , pp. 319 - 330
Copyright
Copyright © Australian Mathematical Society 1999

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