Invariant foliations near normally hyperbolic equilibria for quasilinear parabolic problems

Abstract

We consider quasilinear parabolic evolution equations in the situation where the set of equilibria forms a finite-dimensional C^1-manifold which is normally hyperbolic. The existence of foliations of the stable and unstable manifolds is shown assuming merely C^1-regularity of the underlying equation.

13 pages, 1 figure