System of kinematical conservation laws

Abstract

In a wide range of physical phenomena, we find surfaces Ω t evolving in time t , which need mathematical treat-ment. Here, we briefly review the theory of a system of conservation laws known as the kinematical conservation laws (KCLs), which govern the evolution of these surfaces. KCLs are the most general equations in conservation form which govern the evolution of Ω t with physically realistic singularities. A special type of singularity is a kink, which is a point on Ω t when it is a curve in two dimensions and a curve on Ω t when it is a surface in three dimensions. Across a kink, the normal direction n to Ω t and the normal velocity m of Ω t are discontinuous. This article is aimed at non-experts in the field. Readers may refer to the literature for more details.