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arXiv · 0810.2462

Stability and Total Variation Estimates on General Scalar Balance Laws

Rinaldo M. Colombo·Magali Mercier·Massimiliano D Rosini
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Abstract

Consider the general scalar balance law $\partial_t u + \Div f(t, x,u) = F(t,x,u)$ in several space dimensions. The aim of this note is to estimate the dependence of its solutions from the flow $f$ and from the source $F$. To this aim, a bound on the total variation in the space variables of the solution is obtained. This result is then applied to obtain well posedness and stability estimates for a balance law with a non local source.

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Rinaldo M. Colombo, Magali Mercier, Massimiliano D Rosini. 2008-10-14. Stability and Total Variation Estimates on General Scalar Balance Laws. https://arxiv.org/abs/0810.2462

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