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New entropy conditions for scalar conservation laws with discontinuous flux. (English) Zbl 1228.35144

The author proposes new Kruzhkov type entropy conditions for the scalar conservation law
\[ \partial_t u +\partial_x(H(x)f(u)+H(-x)g(u))=0 \]
with flux function discontinuous at the point \(x=0\). Under assumptions provided the maximum principle, the existence and uniqueness of an entropy admissible weak solution are proven.

MSC:

35L65 Hyperbolic conservation laws
35B50 Maximum principles in context of PDEs
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