Calculus of Variations and Geometric Measure Theory

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
modified on 19 Nov 2022


Published Paper

Inserted: 16 feb 2021
Last Updated: 19 nov 2022

Journal: Zeitschrift für Angewandte Mathematik und Physik
Year: 2022


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.