American Institute of Mathematical Sciences

May  2008, 9(3&4, May): 595-633. doi: 10.3934/dcdsb.2008.9.595

Center manifolds and dynamics near equilibria of quasilinear parabolic systems with fully nonlinear boundary conditions

 1 Department of Mathematics, University of Missouri, Columbia, MO 65211, United States 2 Fachbereich Mathematik und Informatik, Martin-Luther-Universität Halle-Wittenberg, D-06120 Halle 3 Department of Mathematics, University of Karlsruhe, 76128 Karlsruhe, Germany

Received  March 2007 Revised  August 2007 Published  February 2008

We study quasilinear systems of parabolic partial differential equations with fully nonlinear boundary conditions on bounded or exterior domains. Our main results concern the asymptotic behavior of the solutions in the vicinity of an equilibrium. The local center, center–stable, and center–unstable manifolds are constructed and their dynamical properties are established using nonautonomous cutoff functions. Under natural conditions, we show that each solution starting close to the center manifold converges to a solution on the center manifold.
Citation: Yuri Latushkin, Jan Prüss, Ronald Schnaubelt. Center manifolds and dynamics near equilibria of quasilinear parabolic systems with fully nonlinear boundary conditions. Discrete & Continuous Dynamical Systems - B, 2008, 9 (3&4, May) : 595-633. doi: 10.3934/dcdsb.2008.9.595
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