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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 toimprove the results of Colombo, Mercier, Rosini who gave an estimate of thedependence of the solutions from the flow f and from the source F. Theimprovements are twofold: first the expression of the coefficients in theseestimates are more precise; second, we eliminate some regularity hypothesesthus extending significantly the applicability of our estimates.

Improved stability estimates on general scalar balance laws