On gradient flow and entropy solutions for nonlocal transport equations with nonlinear mobility
Analysis of PDEs
2025-09-25 v1
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.
Cite
@article{arxiv.2105.11389,
title = {On gradient flow and entropy solutions for nonlocal transport equations with nonlinear mobility},
author = {Simone Fagioli and Oliver Tse},
journal= {arXiv preprint arXiv:2105.11389},
year = {2025}
}