Condition for explosion triggered by a shock resulting from the expansion of a compressible medium

We present a solution to the problem of the induction of the adiabatic expl osion by a shock resulting from the sudden expansion of an inert medium int o a reactive one. We first calculate the initial velocity and acceleration of the shock, from which we infer the induction time of the explosion, and then a necessary condition for explosion as a constraint on the initial siz e of the expanding medium. (C) Academie des sciences/Elsevier, Paris.