American Institute of Mathematical Sciences

Advanced
2009, 2009(Special): 612-621. doi: 10.3934/proc.2009.2009.612

On normal stability for nonlinear parabolic equations

Jan Prüss 1, , Gieri Simonett 2, and  Rico Zacher 1,

1. 

Fachbereich Mathematik und Informatik, Martin-Luther-Universität Halle-Wittenberg, D-06120 Halle
2. 

Department of Mathematics, Vanderbilt University, Nashville, TN 37240

Received  August 2008 Revised  February 2009 Published  September 2009

We show convergence of solutions to equilibria for quasilinear and fully nonlinear parabolic evolution equations in situations where the set of equilibria is non-discrete, but forms a finite-dimensional $C^1$-manifold which is normally stable.
Keywords: fully nonlinear parabolic equations, generalized principle of linearized stability, normally stable, Convergence towards equilibria, center manifolds.
Mathematics Subject Classification: Primary: 35K55, 35B35, 34G20; Secondary: 37D10, 35R35.
Citation: Jan Prüss, Gieri Simonett, Rico Zacher. On normal stability for nonlinear parabolic equations. Conference Publications, 2009, 2009 (Special) : 612-621. doi: 10.3934/proc.2009.2009.612
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