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We prove the well-posedness of entropy solutions for a wide class of nonlocaltransport equations with nonlinear mobility in one spatial dimension. Thesolution is obtained as the limit of approximations constructed via adeterministic system of interacting particles that exhibits a gradient flowstructure. At the same time, we expose a rigorous gradient flow structure forthis class of equations in terms of an Energy-Dissipation balance, which weobtain via the asymptotic convergence of functionals.

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