Uniform convergence of proliferating particles to the FKPP equation

Autor(es)

Flandoli, Franco ^[1] ; Leimbach, Matti ^[2] ; Olivera, Christian ^[3]

Afiliação do(s) autor(es)

^[1] Univ Pisa, Dipartimento Matemat, Pisa - Italy

^[2] Tech Univ Berlin, Berlin - Germany

^[3] Univ Estadual Campinas, Dept Matemat, Campinas, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Journal of Mathematical Analysis and Applications; v. 473, n. 1, p. 27-52, MAY 1 2019.
• Citações Web of Science: 1

Resumo

In this paper we consider a system of Brownian particles with proliferation whose rate depends on the empirical measure. The dependence is more local than a mean field one and has been called moderate interaction by Oelschlager {[}16], {[}17]. We prove that the empirical process converges, uniformly in the space variable, to the solution of the Fisher-Kolmogorov-Petrowskii-Piskunov equation. We use a semigroup approach which is new in the framework of these systems and is inspired by some literature on stochastic partial differential equations. (C) 2018 Elsevier Inc. All rights reserved. (AU)

• Processo FAPESP: 15/04723-2 - Tópicos em equações diferenciais parciais estocásticas
• Beneficiário: Christian Horacio Olivera
• Modalidade de apoio: Auxílio à Pesquisa - Regular