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Scalar conservation law with discontinuous flux in a bounded domain

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  • We consider the Dirichlet problem for a first-order hyperbolic equation with a convection term discontinuous with respect to the space variable. We introduce a definition of a weak entropy solution to the corresponding problem and then we prove existence and uniqueness of the entropy solution for a class of flux functions. The existence property is obtained by regularization of the flux function while for the uniqueness result we use the method of doubling variables and a Rankine-Hugoniot condition along the line of discontinuity.
    Mathematics Subject Classification: Primary: 35L60, 35B05; Secondary: 35R05.

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