On convergence of solutions to equilibria for quasilinear parabolic problems

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:246

Article

Pruess, Jan²  Simonett, Gieri¹  Zacher, Rico² 

[1] Vanderbilt Univ, Dept Math, Nashville, TN 37240 USA

[2] Univ Halle Wittenberg, Inst Math, D-06120 Halle, Germany

关键词: Quasilinear parabolic equations;    Normally stable;    Center manifolds;    Nonlinear boundary conditions;    Free boundary problems;    Travelling waves;   

DOI  :  10.1016/j.jde.2008.10.034

来源: Elsevier

【 摘 要 】

We show convergence of Solutions to equilibria for quasilinear parabolic evolution equations in situations where the set of equilibria is non-discrete, but forms a finite-dimensional C-1-manifold which is normally hyperbolic. Our results do not depend on the presence of an appropriate Lyapunov functional as in the Lojasiewicz-Simon approach, but are of local nature. (C) 2008 Elsevier Inc. All rights reserved.

【 授权许可】

Free