Topological decoupling and linearization of nonautonomous evolution equations

Christian Pötzsche; Evamaria  Russ

doi:10.3934/dcdss.2016050

Article Contents

2016, Volume 9, Issue 4: 1235-1268. Doi: 10.3934/dcdss.2016050

This issue Previous Article Forced linear oscillators and the dynamics of Euclidean group extensions Next Article

Topological decoupling and linearization of nonautonomous evolution equations

Christian Pötzsche^1, and
Evamaria Russ^1,

1.
Institut für Mathematik, Alpen-Adria Universität Klagenfurt, Universitätsstraße 65-67, 9020 Klagenfurt

Received: June 30, 2015

Revised: August 31, 2015

Published: July 2016

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Abstract

Topological linearization results typically require solution flows rather than merely semiflows. An exception occurs when the linearization fulfills spectral assumptions met e.g. for scalar reaction-diffusion equations. We employ tools from the geometric theory of nonautonomous dynamical systems in order to extend earlier work by Lu [12] to time-variant evolution equations under corresponding conditions on the Sacker-Sell spectrum of the linear part. Our abstract results are applied to nonautonomous reaction-diffusion and convection equations.

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Mathematics Subject Classification: Primary: 37C60; Secondary: 37D10, 37L25.

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