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arXiv · 2405.14565

$L^1$-Contraction Property of Entropy Solutions for Scalar Conservation Laws with Minimal Regularity Assumptions on the Flux

Paz Hashash
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Abstract

This paper is concerned with entropy solutions of scalar conservation laws of the form $\partial_{t}u+\diver f=0$ in $\mathbb{R}^d\times(0,\infty)$. The flux $f=f(x,u)$ depends explicitly on the spatial variable $x$. Using an extension of Kruzkov's method, we establish the $L^1$-contraction property of entropy solutions under minimal regularity assumptions on the flux.

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Paz Hashash. 2024-05-23. $L^1$-Contraction Property of Entropy Solutions for Scalar Conservation Laws with Minimal Regularity Assumptions on the Flux. https://arxiv.org/abs/2405.14565

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