Improved stability estimates on general scalar balance laws

TL;DR

This paper enhances stability estimates for scalar balance laws by refining coefficient expressions and removing regularity constraints, thereby broadening their applicability in multiple space dimensions.

Contribution

It provides more precise stability estimates for solutions of scalar balance laws, extending previous results by reducing regularity assumptions and improving coefficient expressions.

Findings

More accurate coefficients in stability estimates

Elimination of certain regularity hypotheses

Extended applicability to broader classes of solutions

Abstract

Consider the general scalar balance law $\partial_t u + \mathrm{Div} f(t, x, u) = F(t, x, u)$ in several space dimensions. The aim of this note is to improve the results of Colombo, Mercier, Rosini who gave an estimate of the dependence of the solutions from the flow f and from the source F. The improvements are twofold: first the expression of the coefficients in these estimates are more precise; second, we eliminate some regularity hypotheses thus extending significantly the applicability of our estimates.