Conservation law with the flux function discontinuous in the space variable—II

Adimurthi, . ; Mishra, Siddhartha ; Veerappa Gowda, G.D. (2007) Conservation law with the flux function discontinuous in the space variable—II Journal of Computational and Applied Mathematics, 203 (2). pp. 310-344. ISSN 0377-0427

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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 . 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.

Item Type:Article
Source:Copyright of this article belongs to Elsevier Science.
ID Code:119741
Deposited On:16 Jun 2021 13:31
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