Riemann problem for gasdynamic combustion

The Riemann problem for gasdynamic combustion is considered. Existence and uniqueness are obtained constructively for arbitrary Riemann data under the following restrictions: the solutions are selfsimilar and piecewise smooth; the Lax entropy condition is satisfied at the discontinuity points except at the front sides of deflagration waves where the temperatures are assumed to be ignition point; the number of detonation waves in the solutions is as small as possible; the number of times of oscillation of temperature around the ignition point is also as small as possible; and last, the number of deflagration waves is as large as possible. Using the Riemann problem, we analyzed the overtaking of shocks and combustion waves: a shock always accelerates detonation, whereas it transforms deflagration into detonation when it is strong enough. Transition from deflagration to detonation in the ignition problem is also investigated.