Limit relations for three simple hyperbolic systems of conservation laws

作者：Shen, Chun; Sun, Meina^*; Wang, Zhen

来源：Mathematical Methods in the Applied Sciences, 2010, 33(11): 1317-1330.

DOI：10.1002/mma.1248

• delta shock wave
• measure solution
• transport equations
• Euler equations
• the magnetohydrodynamics equations
• Riemann problem
• hyperbolic 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.

• 出版日期2010-7-30
• 单位鲁东大学; 中国科学院武汉物理与数学研究所