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KINEMATICAL CONSERVATION LAWS IN A SPACE OF ARBITRARY DIMENSIONS

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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Official URL: http://dx.doi.org/10.1007/s13226-016-0197-0

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
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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