Non-local scalar conservation laws with discontinuous flux

2020/03/04 by Felisia Angela Chiarello, Chiarello, Felisia Angela, Giuseppe Maria Coclite +1
Mathematics · #Navier-Stokes equation solutions #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.2003.01975

Abstract

We prove the well-posedness of entropy weak solutions for a class of space-discontinuous scalar conservation laws with non-local flux arising in traffic modeling. We approximate the problem adding a viscosity term and we provide L^∞ and BV estimates for the approximate solutions. We use the doubling of variable technique to prove the stability with respect to the initial data from the entropy condition.

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• Stability estimates for non-local scalar conservation laws
• Existence of entropy weak solutions for 1D non-local traffic models with space-discontinuous flux
• Global entropy weak solutions for general non-local traffic flow models with anisotropic kernel
• Stability of quasi-entropy solutions of non-local scalar conservation laws
• Convergence of the numerical approximations and well-posedness: Nonlocal conservation laws with rough flux