Eigenvalues of kinematical conservation laws (KCL) based 3-D weakly nonlinear ray theory (WNLRT)

Arun, KR and Prasad, Phoolan (2010) Eigenvalues of kinematical conservation laws (KCL) based 3-D weakly nonlinear ray theory (WNLRT). In: Applied Mathematics and Computation, 217 (5). pp. 2285-2288.

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Abstract

System of kinematical conservation laws (KCL) govern evolution of a curve in a plane or a surface in space, even if the curve or the surface has singularities on it. In our recent publication K. R. Arun, P. Prasad, 3-D kinematical conservation laws (KCL): evolution of a surface in R-3-in particular propagation of a nonlinear wavefront, Wave Motion 46 (2009) 293-311] we have developed a mathematical theory to study the successive positions and geometry of a 3-D weakly nonlinear wavefront by adding an energy transport equation to KCL. The 7 x 7 system of equations of this KCL based 3-D weakly nonlinear ray theory (WNLRT) is quite complex and explicit expressions for its two nonzero eigenvalues could not be obtained before. In this short note, we use two different methods: (i) the equivalence of KCL and ray equations and (ii) the transformation of surface coordinates, to derive the same exact expressions for these eigenvalues. The explicit expressions for nonzero eigenvalues are important also for checking stability of any numerical scheme to solve 3-D WNLRT. (C) 2010 Elsevier Inc. All rights reserved.

Item Type:	Journal Article
Publication:	Applied Mathematics and Computation
Publisher:	Elsevier Science
Additional Information:	Copyright of this article belongs to Elsevier Science.
Keywords:	Kinematical conservation laws; Ray theory; Nonlinear wave; Polytropic gas; Weakly hyperbolic system.
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	18 Oct 2010 07:23
Last Modified:	18 Oct 2010 07:23
URI:	http://eprints.iisc.ac.in/id/eprint/33289

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