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Conservation law with the flux function discontinuous in the space variable- II - Convex-concave type fluxes and generalized entropy solutions

Adimurthi, * and Mishra, Siddhartha and Gowda, Veerappa GD (2007) Conservation law with the flux function discontinuous in the space variable- II - Convex-concave type fluxes and generalized entropy solutions. In: 1st Indo/Germany Conference on PDE, Scientific Computing and Optimization in Applications, SEP 08-10, 2004, Univ Trier.

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Official URL: http://dx.doi.org/10.1016/j.cam.2006.04.009

Abstract

We deal with a single conservation law with discontinuous convex-concave type fluxes which arise while considering sign changing flux coefficients. The main difficulty is that a weak solution may not exist as the Rankine-Hugoniot condition at the interface may not be satisfied for certain choice of the initial data. We develop the concept of generalized entropy solutions for such equations by replacing the Rankine-Hugoniot condition by a generalized Rankine-Hugoniot condition. The uniqueness of solutions is shown by proving that the generalized entropy solutions form a contractive semi-group in L-1. Existence follows by showing that a Godunov type finite difference scheme converges to the generalized entropy solution. The scheme is based on solutions of the associated Riemann problem and is neither consistent nor conservative. The analysis developed here enables to treat the cases of fluxes having at most one extrema in the domain of definition completely. Numerical results reporting the performance of the scheme are presented. (C) 2006 Elsevier B.V. All rights reserved.

Item Type: Conference Paper
Additional Information: Copyright of this article belongs to Elsevier Science.
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 10 Jun 2010 05:31
Last Modified: 01 Mar 2012 08:50
URI: http://eprints.iisc.ernet.in/id/eprint/26151

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