Reduction principle and asymptotic phase for center manifolds of parabolic systems with nonlinear boundary conditions

Johnson, Russell
Latushkin, Yuri
Schnaubelt, Roland

facul_11; 07

Date: 18. 08. 2010
Abstract:
We prove the reduction principle and study other attractivity properties of the center and center-unstable manifolds in the vicinity of a steady-state solution for quasilinear systems of parabolic partial differential equations with fully nonlinear boundary conditions on bounded or exterior domains.


Primary MSC: 35B35 Stability , 35B40 Asymptotic behavior of solutions
Secondary MSC: 35K52 Initial-boundary value problems for higher-order parabolic systems , 35K60 Nonlinear initial value problems for linear parabolic equations
Keywords: Parabolic system, initial--boundary value problem, invariant manifold, attractivity, stability, center manifold reduction, maximal regularity