Jan Pruess, Gieri Simonett, Rico Zacher
Published 2008-07-09, updated 2008-11-11Version 2
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.
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 fully nonlinear parabolic problems with nonlinear boundary conditions
On the convergence of statistical solutions of the 3D Navier-Stokes-$α$ model as $α$ vanishes
Existence and convergence to a propagating terrace in one-dimensional reaction-diffusion equations
![QR code for arXiv:0807.1539 [math.AP]](http://oss.arxitics.com/images/favicon.svg)