Advanced search
Start date
Betweenand

Semilinear and quasilinear elliptic partial differential equations

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)

Scientific publications
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
BONHEURE, DENIS; GAZZOLA, FILIPPO; DOS SANTOS, EDERSON MOREIRA. PERIODIC SOLUTIONS AND TORSIONAL INSTABILITY IN A NONLINEAR NONLOCAL PLATE EQUATION. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, v. 51, n. 4, p. 3052-3091, 2019. Web of Science Citations: 3.
BONHEURE, DENIS; CASTERAS, JEAN-BAPTISTE; DOS SANTOS, EDERSON MOREIRA; NASCIMENTO, ROBSON. ORBITALLY STABLE STANDING WAVES OF A MIXED DISPERSION NONLINEAR SCHRODINGER EQUATION. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, v. 50, n. 5, p. 5027-5071, 2018. Web of Science Citations: 4.

Please report errors in scientific publications list by writing to: cdi@fapesp.br.