Some qualitative properties of the Riemann problem in gas dynamical combustion

We study the Chapman-Jouguet (CJ) model and the selfsimilar Zeldovich-von Neumann-Döring (SZND) model in chemically reacting gas flows. We discover some basic relationships among ignition temperature T_i, total chemical binding energy Q, and the adibatic exponent γ of polytropic gas. From these relations, we can determine when temperatures along the SZND burning solutions are higher than the ignition temperature T_i. We also study the all possible selfsimilar solutions for the SZND-model. From these results, we can determine when selfsimilar solutions for the CJ-model are the limits of selfsimilar solutions of the SZND model when the reaction rate tends to infinity.