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arXiv · 2105.11389

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

Simone Fagioli·Oliver Tse
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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.

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Simone Fagioli, Oliver Tse. 2021-05-24. On gradient flow and entropy solutions for nonlocal transport equations with nonlinear mobility. https://doi.org/10.1016/j.na.2022.112904

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