Invariant Foliations Near Normally Hyperbolic Equilibria for Quasilinear Parabolic Problems
Jan W. Prüss, Mathias Wilke, Gieri Simonett · Advanced Nonlinear Studies · 2013
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.