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 C1-manifold which is normally hyperbolic. Our results do not depend on the presence of an appropriate Lyapunov functional as in the ojasiewicz-Simon approach, but are of local nature.
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