Inertial manifolds for stochastic pde with dynamical boundary conditions

Peter Brune; Björn Schmalfuss

doi:10.3934/cpaa.2011.10.831

Article Contents

2011, Volume 10, Issue 3: 831-846. Doi: 10.3934/cpaa.2011.10.831

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Inertial manifolds for stochastic pde with dynamical boundary conditions

Peter Brune^1, and
Björn Schmalfuss^1,

1.
Institut für Mathematik, University of Paderborn, 33098 Paderborn

Received: March 31, 2009

Revised: September 30, 2009

Published: April 2011

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Abstract

In this article we investigate the dynamics of stochastic partial differential equations with dynamical boundary conditions. We prove that such a problem with Lipschitz continuous non--linearity generates a random dynamical system. The main result is to show that this random dynamical system has an inertial manifold. Under additional assumptions on the non--linearity this manifold is differentiable.

Keywords:

Random dynamical systems,
inertial manifolds,
stochastic partial differential equations,
dynamical boundary conditions.

Mathematics Subject Classification: Primary: 37L55; Secondary: 60H15, 35B42.

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