Center manifolds and attractivity for quasilinear parabolic problems withfully nonlinear dynamical boundary conditions

Roland Schnaubelt

doi:10.3934/dcds.2015.35.1193

Article Contents

2015, Volume 35, Issue 3: 1193-1230. Doi: 10.3934/dcds.2015.35.1193

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Center manifolds and attractivity for quasilinear parabolic problems with fully nonlinear dynamical boundary conditions

Roland Schnaubelt^1,

1.
Department of Mathematics, Karlsruhe Institute of Technology, 76128 Karlsruhe

Received: February 2014

Revised: June 2014

Published: March 2015

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Abstract

We construct and investigate local invariant manifolds for a large class of quasilinear parabolic problems with fully nonlinear dynamical boundary conditions and study their attractivity properties. In a companion paper we have developed the corresponding solution theory. Examples for the class of systems considered are reaction--diffusion systems or phase field models with dynamical boundary conditions and to the two--phase Stefan problem with surface tension.

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Mathematics Subject Classification: Primary: 35B35, 35B40, 35K59, 35K61; Secondary: 35B65.

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