Optimal mass transport and nonlocal PDEs

• Grant number: 14/23326-1
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: March 01, 2015
• End date: April 08, 2016
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Lucas Catão de Freitas Ferreira
• Grantee: Matheus Correia dos Santos
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated scholarship(s): 15/20962-7 - Optimal Transport Methods in Partial Differential Equation, BE.EP.PD

Abstract

In this project we intend to study the recent developments in the optimal transport theory and its applications to some nonlinear nonlocal partial differential equations. These equations arise from systems where the total mass is conserved, where the individuals of the system interact among themselves and where the model can be identified as a gradient flow on an infinite dimensional manifold with respect to some version of the Wasserstein metric. More specifically, we are interested in the analysis of existence, uniqueness, asymptotic behavior and properties of the steady state of kinetic models like the recent fractional versions of the porous medium equation (involving fractional operators and their inverse operators), semi-discrete and discrete versions of the nonlinear Fokker-Planck equation and the parabolic-parabolic Keller-Segel 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)

FERREIRA, L. C. F.; SANTOS, M. C.; VALENCIA-GUEVARA, J. C.. Minimizing movement for a fractional porous medium equation in a periodic setting. BULLETIN DES SCIENCES MATHEMATIQUES, v. 153, p. 86-117, JUL 2019. (16/16104-8, 14/23326-1)