Inertial manifolds with delay for retarded semilinear parabolic equations

A. V. Rezounenko

doi:10.3934/dcds.2000.6.829

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2000, Volume 6, Issue 4: 829-840. Doi: 10.3934/dcds.2000.6.829

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Inertial manifolds with delay for retarded semilinear parabolic equations

A. V. Rezounenko^1,

1.
Department of Mechanics and Mathematics, Kharkov University, 4 Svobody sqr., 61077, Kharkov

Received: April 30, 1999

Revised: March 31, 2000

Published: September 2000

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Abstract

We consider the system of parabolic equations with distributed delay. The existence of Inertial Manifolds with Delay is proved. We prove that the system has finite number of determining modes and can be reproduced by a finite-dimensional system with concerntrated delays.

Keywords:

Inertial manifolds with delay,
retarded non-linear PDEs.

Mathematics Subject Classification: Primary: 35B40, 35R10, 58D25.

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