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System of kinematical conservation laws (KCL) a review article

In a wide range of physical phenomena, we find propagating surfaces Ωt which need mathematical treatment. In this article, we review the theory of the system of kinematical conservation laws (KCL), which govern the evolution of these surfaces and have been developed by the second author and his collaborators. KCL are the most general equations in conservation form, governing the evolution of Ωt with physically realistic singularities. A very special type of singularity is a kink, which is a point on Ωt when Ωt is a curve in R2 andisacurveonΩt whenΩt isasurfaceinR3. AcrossakinkthenormalntoΩt and the normal velocity m on Ωt are discontinuous. The main aim of this article is to identify density of the conserved variable and the flux for the KCL which we did not do earlier. The presentation of this article is like that in a popular article, which which aims at non-experts in the field.

preprint2022arXivOpen access
K. R. ArunPhoolan Prasad
math.AP
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K. R. ArunPhoolan Prasad

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