On convergence of solutions to equilibria for quasilinear parabolic problems

Jan Pruess; Gieri Simonett; Rico Zacher

doi:10.1016/j.jde.2008.10.034

On convergence of solutions to equilibria for quasilinear parabolic problems

Analysis of PDEs 2016-12-20 v2 Classical Analysis and ODEs

Authors: 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.

Keywords

quasilinear parabolic equations convergence to equilibria normally hyperbolic manifold finite-dimensional manifold lyapunov functional local convergence

Cite

@article{arxiv.0807.1539,
  title  = {On convergence of solutions to equilibria for quasilinear parabolic problems},
  author = {Jan Pruess and Gieri Simonett and Rico Zacher},
  journal= {arXiv preprint arXiv:0807.1539},
  year   = {2016}
}

Comments

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

On convergence of solutions to equilibria for quasilinear parabolic problems

Abstract

Keywords

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