On normal stability for nonlinear parabolic equations
Jan Prüss - 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
Received: August 2008; Revised: February 2009; Published: September 2009.