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Asymptotic dynamics of delayed nonlinear reaction and diffusion equations

Grant number: 07/00029-8
Support type:Scholarships abroad - Research
Effective date (Start): May 15, 2007
Effective date (End): August 14, 2007
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Analysis
Principal researcher:Sergio Muniz Oliva Filho
Grantee:Sergio Muniz Oliva Filho
Host: Neus Cónsul Porras
Home Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
Research place: Universitat Politècnica de Catalunya (UPC), Spain  

Abstract

We intend to continue the existing cooperation between the two Institutions. For this trip in particular, we have two problems in mind, first that it concerns to the problem of reaction and diffusion with logistic non linearity in the border, involving delays. The objective is to confirm the existence of Hopf bifurcations as we increase the delay. There are evidences of chaotic behavior for some parameters, behavior that doesn’t exist when the reaction is in the interior. Another very interesting problem, is the existence or not of patterns in convex domains for reaction diffusion equations with the non linearity in the border. There exist results showing the non existence in the case of a ball and the existence in the case of squares. (AU)

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