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Interactions of delta shock waves in a strictly hyperbolic system of conservation laws. (English) Zbl 1155.35059

The authors consider the Riemann problem for a strictly hyperbolic system of two conservation laws from magnetohydrodynamics. The system is considered from the point of view of weak solutions. Generally a solution to such problem is a combination of shock waves, contact discontinuities, rarefaction waves, and delta shock waves. It is shown how the solutions continue beyond points of interaction of these types of solutions. A type of generalized solution is introduced: delta contact discontinuity. A complete description of all global solutions with initial data given by two jump points and three constant states is presented.

MSC:

35L65 Hyperbolic conservation laws
35L67 Shocks and singularities for hyperbolic equations
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