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A note on a parabolic equation with nonlinear dynamical boundary condition

Please always quote using this URN:urn:nbn:de:0296-matheon-10709
  • We consider a semilinear parabolic equation subject to a nonlinear dynamical boundary condition that is related to the so-calles Wentzell boundary condition. First, we prove the existence and uniqueness of global solutions as well as the existence of a global attractor. Then we derive a suitable Lojasiewicz-Simon-type inequality to show the convergence of global solutions to single steady states as time tends to infinity under the assumption that the nonlinear terms $f$, $g$ are real analytic. Moreover, we provide an estimate for the convergence rate.

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Metadaten
Author:Jürgen Sprekels, Hao Wu
URN:urn:nbn:de:0296-matheon-10709
Referee:Fredi Tröltzsch
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2012/03/09
Release Date:2012/03/09
Tag:Lojasiewicz-Simon inequality; convergence to equilibrium; dynamical boundary condition; global attractor; parabolic equation
Institute:Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS)
MSC-Classification:35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Bxx Qualitative properties of solutions / 35B40 Asymptotic behavior of solutions
35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Bxx Qualitative properties of solutions / 35B41 Attractors
35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Bxx Qualitative properties of solutions / 35B45 A priori estimates
Preprint Number:949
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