Improved stability estimates on general scalar balance laws

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.

Correction sur le coefficient ${\kappa }^{\ast }$

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