Limit relations for three simple hyperbolic systems of conservation laws

摘要

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 d-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 e tends to zero. Furthermore, the result can also be generalized to more general situations.