Preprint 2002-056

Conservation Laws with Time Dependent Discontinuous Coefficients

Giuseppe Maria Coclite and Nils Henrik Risebro

Abstract: We consider scalar conservation laws where the flux function depends discontinuously on both the spatial and temporal location. Our main results are the existence and well--posedness of an entropy solution to the Cauchy problem. The existence is established by showing that a sequence of front tracking approximations is compact in $L^1$, and that the limits are entropy solutions. Then, using the definition of an entropy solution taken form \cite{KarlsenTowersRisebro:stable}, we show that the solution operator is $L^1$ contractive. These results generalize the corresponding results of Kruzhkov and Towers et al.

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Giuseppe Maria Coclite, <>
Nils Henrik Risebro, <>
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<> December 18 2002.

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