On the chain rule formulas for divergences and applications to conservation laws. (April 2017) - Crasta, Graziano; De Cicco, Virginia
Abstract: In this paper we prove a nonautonomous chain rule formula for the distributional divergence of the composite function v ( x ) = B ( x, u ( x ) ), where B ( ⋅, 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.