# American Institute of Mathematical Sciences

March  2013, 12(2): 755-769. doi: 10.3934/cpaa.2013.12.755

## The Riemann problem of conservation laws in magnetogasdynamics

 1 Department of Mathematics, Shanghai University, Shanghai, 200444, China

Received  July 2011 Revised  July 2012 Published  September 2012

In this paper, we study the Riemann problem for a simplified model of one dimensional ideal gas in magnetogasdynamics. By using the characteristic analysis method, we prove the global existence of solutions to the Riemann problem constructively under the Lax entropy condition. The image of contact discontinuity in magnetogasdynamics is a curve with $u=Const.$ in the $(\tau,p,u)$ space. Its projection on the $(p,u)$ plane is a straight line that parallels to the $p$-axis. In contrast with the problem in gas dynamics, the result causes more complicated and difficult than that in gas dynamics.
Citation: Yanbo Hu, Wancheng Sheng. The Riemann problem of conservation laws in magnetogasdynamics. Communications on Pure & Applied Analysis, 2013, 12 (2) : 755-769. doi: 10.3934/cpaa.2013.12.755
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