A chain rule formula in BV and applications to conservation laws

Abstract

In this paper we prove a new chain rule formula for the distributional derivative of the composite function $v(x)=B(x,u(x))$, where $u:]a,b[\to {\mathbb{R}}^d$ has bounded variation, $B(x,\cdot )$ is continuously differentiable and $B(\cdot ,u)$ has bounded variation. We propose an application of this formula in order to deal in an intrinsic way with the discontinuous flux appearing in conservation laws in one space variable.

26 pages

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