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Pre-Publicación 2021-09

Felisia A. Chiarello, Luis M. Villada:

On existence of entropy solutions for 1D nonlocal conservation laws with space-discontinous flux

Abstract:

We prove the well-posedness of entropy weak solutions for a class of 1D space-discontinuous scalar conservation laws with non-local flux, describing traffic flow on roads with rough conditions. We approximate the problem through a Godunov-type numerical scheme and provide $\mathbf{L}^\infty$ and $\mathbf{BV}$ estimates for the approximate solutions. The limit model as the kernel support tends to zero is numerically investigated.

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