On gradient flow and entropy solutions for nonlocal transport equations with nonlinear mobility
Simone Fagioli, Oliver Tse
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.
Topics & Concepts
Balanced flowNonlinear systemDissipationEntropy (arrow of time)MathematicsFlow (mathematics)Statistical physicsMathematical analysisLimit (mathematics)Convergence (economics)Energy balanceApplied mathematicsPhysicsGeometryThermodynamicsQuantum mechanicsEconomicsEconomic growthGeometric Analysis and Curvature FlowsNonlinear Partial Differential EquationsMathematical Biology Tumor Growth