Systems of partial differential equations and nonlinear elliptic equations
Semilinear equations with absorption nonlinearities and measures as data
Stability and hyperbolicity of equilibria for a nonlocal quasilinear Chafee-Infant...
Grant number: | 16/50453-0 |
Support Opportunities: | Regular Research Grants |
Field of knowledge: | Physical Sciences and Mathematics - Mathematics - Analysis |
Agreement: | Fonds de la Recherche Scientifique (F.R.S.- FNRS) |
Mobility Program: | SPRINT - Projetos de pesquisa - Mobilidade |
Principal Investigator: | Ederson Moreira dos Santos |
Grantee: | Ederson Moreira dos Santos |
Principal researcher abroad: | Denis Bonheure |
Institution abroad: | Université Libre de Bruxelles (ULB), Belgium |
Host Institution: | Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil |
Associated research grant: | 15/17096-6 - Problems on Elliptic PDEs: systems and equations, AP.R |
Abstract
The purpose of the present project is to allow the continuation and the development of the collaboration between Brazilian and Belgian researchers in the field of partial differential equations (PDEs). This collaboration has already some history: Ederson Moreira dos Santos (USP São Carlos), coordinator on the Brazilian side, and Denis Bonheure (ULB), coordinator on the Belgian side, have been working together for about 8 years, whereas Djairo de Figueiredo (UNICAMP) and Jean-Pierre Gossez (ULB) have been collaborating for more than 30 years. A significant number (over 20) of joint publications in prestigious international journals have been produced over the years, for instance in Communications in Partial Differential Equations, Journal of Functional Analysis, Journal of the European Mathematical Society, Journal de Mathématiques Pures et Appliqués, Journal of Differential Equations, Transactions of the American Mathematical Society and others. The research, which will be pursued, concerns the theoretical study of some nonlinear PDEs, although numerical simulations will be realized occasionally. PDEs are often the main ingredients in mathematical models. They appear naturally in physics, biology, chemistry, and are used by now in mathematical models in finance. We will mainly study PDEs of elliptic or parabolic type. Parabolic PDEs help to understand the evolution in time of the model while elliptic PDEs are more concerned with the behavior of the model in the long run (for instance it is related to stable configurations of the system). (AU)
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