On gradient flow and entropy solutions for nonlocal transport equations with nonlinear mobility

We prove the well-posedness of entropy solutions for a wide class of nonlocaltransport equations with nonlinear mobility in one spatial dimension. The solutionis obtained as the limit of approximations constructed via a deterministic systemof 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 ofan Energy-Dissipation balance, which we obtain via the asymptotic convergenceof functionals.(c) 2022 The Author(s). Published by Elsevier Ltd. This is an open access article underthe CC BY license (http://creativecommons.org/licenses/by/4.0/).