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

created by denitti on 16 Feb 2021

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Submitted Paper

Inserted: 16 feb 2021
Last Updated: 16 feb 2021

Year: 2021

Abstract:

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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