Prasad, Phoolan
(2016)
*KINEMATICAL CONSERVATION LAWS IN A SPACE OF ARBITRARY DIMENSIONS.*
In: INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS, 47
(4).
pp. 641-653.

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## 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 Omega(t) in d-dimensional x-space, where x = (x(1), x(2),..., x(d)) is an element of R-d. The KCL are derived in a specially defined ray coordinates (xi = (xi(1), xi(2),..., xi(d-1)), t), where xi(1), xi(2),..., xi(d-1) are surface coordinates on Omega(t) and t is time. KCL are the most general equations in conservation form, governing the evolution of Omega(t) with physically realistic singularities. A very special type of singularity is a kink, which is a point on Omega(t) when Omega(t) is a curve in R-2 and is a curve on Omega(t) when it is a surface in R-3. Across a kink the normal n to Omega(t) and normal velocity m on Omega(t) are discontinuous.

Item Type: | Journal Article |
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Additional Information: | Copy right for this article belongs to the INDIAN NAT SCI ACAD, BAHADUR SHAH ZAFAR MARG, NEW DELHI 110002, INDIA |

Department/Centre: | Division of Physical & Mathematical Sciences > Mathematics |

Depositing User: | Id for Latest eprints |

Date Deposited: | 17 Feb 2017 07:27 |

Last Modified: | 17 Feb 2017 07:27 |

URI: | http://eprints.iisc.ac.in/id/eprint/56256 |

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