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| Title: | A note on a parabolic equation with nonlinear dynamical boundary condition |
| Authors: | Sprekels, Jürgen; Wu, Hao |
| Issue Date: | 2008 |
| Published in: | Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik , Volume 1378, ISSN 0946-8633 |
| Publisher: | Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik |
| Abstract: | We consider a semilinear parabolic equation subject to a nonlinear dynamical boundary condition that is related to the so-called 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. |
| Keywords: | Parabolic equation; dynamical boundary condition; global attractor; convergence to equilibrium; Lojasiewicz-Simon inequality |
| DDC: | 510 |
| License: | This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties. Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden. |
| Appears in Collections: | Mathematik |
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