The Generalized Riemann Problem for a Simplified Model in Magnetogasdynamics

摘要

We consider the generalized Riemann problemfor one dimensional ideal gas in Magnetogasdynamics in aneighborhood of the origin (t > 0) in the (x,t) plane. Accordingto the different cases of the corresponding Riemann solutions,we construct uniquely the perturbed solutions. We observethat the contact discontinuity appears for some cases afterperturbation while there is no contact discontinuity of thecorresponding Riemann solution. For most cases, the Riemannsolutions are stable under such local small perturbations on theRiemann initial data. While for some few cases, the forward(backward) rarefaction wave can be transformed into theforward (backward) shock wave which reveal the instabilityof the Riemann solutions.