Asymptotic dynamics of delayed nonlinear reaction and diffusion equations

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