The Riemann problem of conservation laws in magnetogasdynamics

In this paper, we study the Riemann problem for a simplified modelof one dimensional ideal gas in magnetogasdynamics. By using thecharacteristic analysis method, we prove the global existence of solutions to the Riemann problem constructively underthe Lax entropy condition. The image of contact discontinuity inmagnetogasdynamics is a curve with $u=Const.$ in the $(\tau,p,u)$ space. Itsprojection on the $(p,u)$ plane is a straight line that parallels tothe $p$-axis. In contrast with the problem in gas dynamics, theresult causes more complicated and difficult than that in gasdynamics.