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.


35L65 Hyperbolic conservation laws
35L67 Shocks and singularities for hyperbolic equations
Full Text: DOI


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