The Generalized Riemann Problem for the Simplified Model in Magnetogasdynamics with Combustion

摘要

We consider the generalized Riemann problem forthe simplified combustible model in magnetogasdynamics ina neighborhood of the origin (t > 0) in the (x, t) plane.In the light of the different Riemann solutions situations, weobtain the unique solutions after perturbation. We observe thatthere are essential differences between the above two cases. Weobtain that the transition between the detonation wave andthe deflagration wave occurs. Although the combustion wavedoes not appear in the corresponding Riemann problem, theperturbed combustion wave may appear, which shows that theunburnt gas is unstable.