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Journal of Dynamics and Differential Equations

, Volume 21, Issue 3, pp 371–415 | Cite as

A Smooth Center Manifold Theorem which Applies to Some Ill-Posed Partial Differential Equations with Unbounded Nonlinearities

  • Rafael de la LlaveEmail author
Article

Abstract

We prove the existence of a smooth center manifold for several partial differential equations, including ill posed equations with unbounded nonlinearities. We also prove smooth dependence on parameters with respect to some perturbations, including unbounded ones. More concretely, we prove an abstract theorem and present applications to several concrete equations: ill posed Boussinesq, equation and system and nonlinear Laplace equations in cylindrical domains. We also consider the effect of some geometric structures.

Keywords

Center manifolds Ill posed equations Boussinesq equations Reduction principles 

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© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of TexasAustinUSA

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