TRANSITION FROM A DEFLAGRATION TO A DETONATION IN GAS DYNAMIC COMBUSTION

The transition from a deflagration to a detonation (DDT) in gas dynamics is investigated through the process of a deflagration with a imite width flame overtaken by a shock. The problem is formulated as a free boundary value problem in an angular domain with a strong detonation and a reflected shock as boundaries. The main difficulty lies in the fact that the strength of reflected shock is zero at the vertex where the shock speed degenerates to be the same as the characteristic speed. The conclusion is that a strong detonation and a retonation (a reflected shock) form locally. Also the entropy satisfaction of this solution is presented.