On convergence of solutions to equilibria for quasilinear parabolic problems

Abstract

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 Łojasiewicz-Simon approach, but are of local nature.

33 pages. To appear in Journal of Differential Equations. Contains a more general result in Theorem 6.1 than the first version

References in corpus (1)

• On normal stability for nonlinear parabolic equations

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