Reduction Principle and Asymptotic Phase for Center Manifolds of Parabolic Systems with Nonlinear Boundary Conditions

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• 作者：Russell Johnson (1)
  Yuri Latushkin (2)
  Roland Schnaubelt (3)
  
• 关键词：Parabolic system ; Initial ; boundary value problem ; Invariant manifold ; Attractivity ; Stability ; Center manifold reduction ; Maximal regularity ; Primary ; 35B35 ; 35B40 ; Secondary ; 35K50 ; 35K60
• 刊名：Journal of Dynamics and Differential Equations
• 出版年：2014
• 出版时间：June 2014
• 年：2014
• 卷：26
• 期：2
• 页码：243-266
• 全文大小：
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• 作者单位：Russell Johnson (1)
  Yuri Latushkin (2)
  Roland Schnaubelt (3)
  
  1. Dipartimento di Sistemi e Informatica, Universita di Firenze, Florence, 50139, Italy
  2. Department of Mathematics, University of Missouri, Columbia, MO聽, 65211, USA
  3. Department of Mathematics, Karlsruhe Institute of Technology, 76128聽, Karlsruhe, Germany
  
• ISSN：1572-9222

文摘

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.