A regularity theorem for a non-convex scalar conservation law
In this paper we study the regularity properties of solutions of a single conservation law. We prove that if the flux function \(f(\cdot)\) is smooth and totally nonlinear in the sense that f''(\(\cdot)\) vanishes at isolated points only, and if the initial data \(u_ 0(\cdot)\) is bounded and measurable, then f'(\(u(\cdot,t))\) is in the class of functions of locally bounded variation for all \(t>0\).
scientific article; zbMATH DE number 3867739