`a`
Discrete and Continuous Dynamical Systems - Series A (DCDS-A)
 

Center manifolds and attractivity for quasilinear parabolic problems with fully nonlinear dynamical boundary conditions

Pages: 1193 - 1230, Volume 35, Issue 3, March 2015      doi:10.3934/dcds.2015.35.1193

 
       Abstract        References        Full Text (695.7K)       Related Articles       

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.
Mathematics Subject Classification:  Primary: 35B35, 35B40, 35K59, 35K61; Secondary: 35B65.

Received: February 2014;      Revised: June 2014;      Available Online: October 2014.

 References