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arXiv · 1605.09005

On the chain rule formulas for divergences and applications to conservation laws

Graziano Crasta·Virginia De Cicco
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Abstract

In this paper we prove a nonautonomous chain rule formula for the distributional divergence of the composite function $\boldsymbol{v}(x)=\boldsymbol{B}(x,u(x))$, where $\boldsymbol{B}(\cdot,t)$ is a divergence--measure vector field and $u$ is a function of bounded variation. As an application, we prove a uniqueness result for scalar conservation laws with discontinuous flux.

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Graziano Crasta, Virginia De Cicco. 2016-05-29. On the chain rule formulas for divergences and applications to conservation laws. https://doi.org/10.1016/j.na.2016.10.005

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