Invariant foliations near normally hyperbolic equilibria for quasilinear parabolic problems

2012/06/06 by Jan Pruess, Pruess, Jan, Gieri Simonett +3
Computer Science · Engineering · Mathematics · #34G20 #35B35 #35K55 #35R35 #37D10 #37D30 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #Dynamical Systems (math.DS) #FOS: Mathematics #Nonlinear Partial Differential Equations #Stability and Controllability of Differential Equations #math.AP #math.DS #msc:34G20 #msc:35B35 #msc:35K55 #msc:35R35 #msc:37D10 #msc:37D30

paper · pdf · doi:10.48550/arxiv.1206.1162

13 pages, 1 figure

arxiv created 2012/06/06 · openalex publication_date 2012/06/06 · arxiv updated 2012/06/07 · openalex created_date 2022/09/30 · openalex updated_date 2026/07/28

Abstract

We consider quasilinear parabolic evolution equations in the situation where the set of equilibria forms a finite-dimensional C¹-manifold which is normally hyperbolic. The existence of foliations of the stable and unstable manifolds is shown assuming merely C¹-regularity of the underlying equation.

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