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arXiv · 0807.1539

On convergence of solutions to equilibria for quasilinear parabolic problems

Jan Pruess·Gieri Simonett·Rico Zacher
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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 \L ojasiewicz-Simon approach, but are of local nature.

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Jan Pruess, Gieri Simonett, Rico Zacher. 2008-07-09. On convergence of solutions to equilibria for quasilinear parabolic problems. https://doi.org/10.1016/j.jde.2008.10.034

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