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

created by denitti on 16 Feb 2021
modified on 19 Nov 2022

[BibTeX]

Published Paper

Inserted: 16 feb 2021
Last Updated: 19 nov 2022

Journal: Zeitschrift für Angewandte Mathematik und Physik
Year: 2022
Doi: https://doi.org/10.1007/s00033-022-01766-0

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.