Center manifolds and attractivity for quasilinear parabolic problems with
fully nonlinear dynamical boundary conditions
Roland Schnaubelt - Department of Mathematics, Karlsruhe Institute of Technology, 76128 Karlsruhe, Germany (email)
Abstract: We construct and investigate local invariant manifolds for a large class of quasilinear parabolic problems with fully nonlinear dynamical boundary conditions and study their attractivity properties. In a companion paper we have developed the corresponding solution theory. Examples for the class of systems considered are reaction--diffusion systems or phase field models with dynamical boundary conditions and to the two--phase Stefan problem with surface tension.
Keywords: Parabolic system, Stefan problem, dynamical boundary conditions,
exponential dichotomy and trichotomy, invariant manifold, center manifold, stability.
Received: February 2014; Revised: June 2014; Available Online: October 2014.
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