A smooth center manifold theorem which applies to some III-posed partial differential equations with unbounded nonlinearities
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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.
CitationDe La Llave, R. A smooth center manifold theorem which applies to some III-posed partial differential equations with unbounded nonlinearities. "Journal of dynamics and differential equations", 2009, vol. 21, núm. 3, p. 371-415.
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