Interactions of delta shock waves in a strictly hyperbolic system of conservation laws

Abstract

We study interaction of generalized solutions to a strictly hyperbolic system of two conservation laws from magnetohydrodynamics. The Riemann problem of this system is known to be solvable by a combination of shock waves, contact discontinuities, rarefaction waves and delta shock waves. We derive how the solutions continue beyond points of interaction of these types of solutions. We introduce a type of generalized solution, a delta contact discontinuity. A complete description of all global solutions with initial data given by two jump points and three constant states is obtained. © 2008 Elsevier Inc. All rights reserved.