Detonation wave solutions to the scalar combustion models with a singular source term

Abstract

This paper is concerned with detonation wave solutions of scalar combustion models with a singular source term to the Chapman–Jouguet (CJ) and the Zeldovich–von Neumann–Döring (ZND) reaction equations, respectively. The self-similar detonation wave solution to a Riemann initial-boundary value problem for the simplest CJ combustion model is constructed. The existence of a global in time classical solution to a free boundary value problem for the scalar ZND model is obtained by using the iterative method. Furthermore, we obtain that as the reaction rate goes to infinity, the detonation wave solution of the scalar ZND combustion model converges to a detonation wave solution of the corresponding CJ combustion model. The results are keeping with the fact that, in an actual spherical detonation process, the detonation front is propagated with a speed less than that derived from the CJ hypothesis, which is stated in Sec. 163 in the book Supersonic Flow and Shock Waves.