Existence and stability of entropy solutions for a conservation law with discontinuous non-convex fluxes
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Centre for Applicable Mathematics, Tata Institute of Fundamental Research, Post Bag No 6503, Sharadanagar, Bangalore - 560065
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Center of Mathematics for Applications, University of Oslo, P.O. Box 1053, Oslo
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3.
TIFR center, IISc Campus, P.O. Box 1234, Bangalore
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Received:
01 August 2006
Revised:
01 November 2006
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Primary: 35L65, 65M12.
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We consider a scalar conservation law with a discontinuous flux function. The fluxes are non-convex, have multiple points of extrema and can have arbitrary intersections. We propose an entropy formulation based on interface connections and associated jump conditions at the interface. We show that the entropy solutions with respect to each choice of interface connection exist and form a contractive semi-group in $L^1$. Existence is shown by proving convergence of a Godunov type scheme by a suitable modification of the singular mapping approach. This extends the results of [3] to the general case of non-convex flux geometries.
Citation: . Adimurthi, Siddhartha Mishra, G.D. Veerappa Gowda. Existence and stability of entropy solutions for a conservation law with discontinuous non-convex fluxes[J]. Networks and Heterogeneous Media, 2007, 2(1): 127-157. doi: 10.3934/nhm.2007.2.127
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Abstract
We consider a scalar conservation law with a discontinuous flux function. The fluxes are non-convex, have multiple points of extrema and can have arbitrary intersections. We propose an entropy formulation based on interface connections and associated jump conditions at the interface. We show that the entropy solutions with respect to each choice of interface connection exist and form a contractive semi-group in $L^1$. Existence is shown by proving convergence of a Godunov type scheme by a suitable modification of the singular mapping approach. This extends the results of [3] to the general case of non-convex flux geometries.
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