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Kinematical conservation laws in a space of arbitrary dimensions

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  • Phoolan Prasad

    (Indian Institute of Science)

Abstract

In a large number of physical phenomena, we find propagating surfaces which need mathematical treatment. In this paper, we present the theory of kinematical conservation laws (KCL) in a space of arbitrary dimensions, i.e., d-D KCL, which are equations of evolution of a moving surface Ωt in d-dimensional x-space, where x = (x 1, x 2,..., x d) ∈ Rd. The KCL are derived in a specially defined ray coordinates (ξ = (ξ1, ξ2,..., ξd−1), t), where ξ1, ξ2,..., ξd−1 are surface coordinates on Ωt and t is time. 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 and is a curve on Ωt when it is a surface in R3. Across a kink the normal n to Ωt and normal velocity m on Ωt are discontinuous.

Suggested Citation

  • Phoolan Prasad, 2016. "Kinematical conservation laws in a space of arbitrary dimensions," Indian Journal of Pure and Applied Mathematics, Springer, vol. 47(4), pages 641-653, December.
    • Handle: RePEc:spr:indpam:v:47:y:2016:i:4:d:10.1007_s13226-016-0197-0
    DOI: 10.1007/s13226-016-0197-0
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