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System of kinematical conservation laws
In a wide range of physical phenomena, we find surfaces Wt evolving in time t, which need mathematical treatment. 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 Wt with physically realistic singularities. A special type of singularity is a kink, which is a point on Wt when it is a curve in two dimensions and a curve on Wt when it is a surface in three dimensions. Across a kink, the normal direction n to Wt and the normal velocity m of Wt are discontinuous. This article is aimed at non-experts in the field. Readers may refer to the literature for more details
Keywords
Curves and surfaces, kinematical conserva-tion laws, kink, ray theory.
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