Estimates on the distance of inertial manifolds

José M. Arrieta; Esperanza Santamaría

doi:10.3934/dcds.2014.34.3921

Article Contents

2014, Volume 34, Issue 10: 3921-3944. Doi: 10.3934/dcds.2014.34.3921

This issue Previous Article Asymptotic behaviour of a non-autonomous Lorenz-84 system Next Article Pathwise solutions and attractors for retarded SPDEs with time smooth diffusion coefficients

Estimates on the distance of inertial manifolds

José M. Arrieta^1, and
Esperanza Santamaría^1,

1.
Departamento de Matemática Aplicada, Universidad Complutense de Madrid, 28040 Madrid

Received: February 28, 2013

Revised: April 30, 2013

Published: September 2014

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Abstract

In this paper we obtain estimates on the distance of inertial manifolds for dynamical systems generated by evolutionary parabolic type equations. We consider the situation where the systems are defined in different phase spaces and we estimate the distance in terms of the distance of the resolvent operators of the corresponding elliptic operators and the distance of the nonlinearities of the equations.

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Mathematics Subject Classification: Primary: 35B42, 35K90.

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