On gradient flow and entropy solutions for nonlocal transport equations with nonlinear mobility. (August 2022)

• Record Type: Journal Article
• Authors: Fagioli, Simone; Tse, Oliver
• Is Part Of: Nonlinear analysis. Volume 221(2022)
• Publication Date: 2022-08
• Subjects: 35A15 -- 35A35 -- 35D30 -- 45K05 -- 65M75; Deterministic particle approximation -- Entropy solutions -- Gradient flow -- Nonlocal transport equations; 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.2022.112904
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We prove the well-posedness of entropy solutions for a wide class of nonlocal transport equations with nonlinear mobility in one spatial dimension. The solution is obtained as the limit of approximations constructed via a deterministic system of interacting particles that exhibits a gradient flow structure. At the same time, we expose a rigorous gradient flow structure for this class of equations in terms of an Energy-Dissipation balance, which we obtain via the asymptotic convergence of functionals.