Stability and Total Variation Estimates on General Scalar Balance Laws

Details Stability and Total Variation Estimates on General Scalar Balance Laws Stability and Total Variation Estimates on General Scalar Balance Laws

2008-10-14

arxiv.org/abs/0810.2462v1

Mathematics

Analysis of PDEs

Scientific paper

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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