Limit relations for three simple hyperbolic systems of conservation laws

This paper is concerned with the limit relations from the Euler equations of one-dimensional compressible fluid flow and the magnetohydrodynamics equations to the simplified transport equations, where the delta-shock waves occur in their Riemann solutions of the latter two equations. The objective is to prove that the Riemann solutions of the perturbed equations coming from the one-dimensional simplified Euler equations and the magnetohydrodynamics equations converge to the corresponding Riemann solutions of the simplified transport equations as the perturbation parameterx epsilon tends to zero. Furthermore, the result can also be generalized to more general situations. Copyright (C) 2009 John Wiley & Sons, Ltd.