Calculus of Variations and Geometric Measure Theory
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G. M. Coclite - N. De Nitti - A. Keimer - L. Pflug

On existence and uniqueness of weak solutions to nonlocal conservation laws with BV kernels

created by denitti on 16 Feb 2021


Submitted Paper

Inserted: 16 feb 2021
Last Updated: 16 feb 2021

Year: 2021


In this note, we extend the known results on the existence and uniqueness of weak solutions to conservation laws with nonlocal flux. In case the nonlocal term is given by a convolution $\gamma \ast q$, we weaken the standard assumption on the kernel $\gamma \in L^\infty\big((0,T); W^{1,\infty}(\mathbb R)\big)$ to the substantially more general condition $\gamma \in L^\infty((0,T); BV(\mathbb R))$, which allows for discontinuities in the kernel.

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