Nonlinear degenerate cross-diffusion systems with nonlocal interaction. (April 2018)

• Record Type: Journal Article
• Authors: Di Francesco, M.; Esposito, A.; Fagioli, S.
• Is Part Of: Nonlinear analysis. Volume 169(2018)
• Page Start: 94
• Page End: 117
• Publication Date: 2018-04
• Subjects: Cross-diffusion systems -- Nonlocal interaction -- JKO scheme; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2017.12.003
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We investigate a class of systems of partial differential equations with nonlinear cross-diffusion and nonlocal interactions, which are of interest in several contexts in social sciences, finance, biology, and real world applications. Assuming a uniform "coerciveness" assumption on the diffusion part, which allows to consider a large class of systems with degenerate cross-diffusion (i.e. of porous medium type) and relaxes sets of assumptions previously considered in the literature, we prove global-in-time existence of weak solutions by means of a semi-implicit version of the Jordan–Kinderlehrer–Otto scheme. Our approach allows to consider nonlocal interaction terms not necessarily yielding a formal gradient flow structure.