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On normal stability for nonlinear parabolic equations

Pages: 612 - 621, Issue Special, September 2009

 Abstract        Full Text (185.5K)              

Jan Prüss - Fachbereich Mathematik und Informatik, Martin-Luther-Universität Halle-Wittenberg, D-06120 Halle, Germany (email)
Gieri Simonett - Department of Mathematics, Vanderbilt University, Nashville, TN 37240, United States (email)
Rico Zacher - Fachbereich Mathematik und Informatik, Martin-Luther-Universität Halle-Wittenberg, D-06120 Halle, Germany (email)

Abstract: 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:  Convergence towards equilibria, normally stable, generalized principle of linearized stability, center manifolds, fully nonlinear parabolic equations
Mathematics Subject Classification:  Primary: 35K55, 35B35, 34G20; Secondary: 37D10, 35R35

Received: August 2008;      Revised: February 2009;      Published: September 2009.