Structure of Entropy Solutions for Multi{dimensional Scalar Conservation Laws
نویسنده
چکیده
An entropy solution u of a multi{dimensional scalar conservation law is not necessarily in BV , even if the conservation law is genuinely nonlinear. We show that u nevertheless has the structure of a BV {function in the sense that the shock location is codimension{one rectiiable. This result highlights the regularizing eeect of genuine non-linearity in a qualitative way; it is based on the locally nite rate of entropy dissipation. The proof relies on the geometric classiication of blow{ups in the framework of the kinetic formulation. 1. Introduction In this paper, we study the structure of entropy solutions of scalar conservation laws in n space dimensions @ t u + div x f(u) = 0. A bounded measurable entropy solution u is characterized by dissipation of entropy
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