Properties of Detonation Waves

this article the behavior of the solution with varying ratio of these two scales is studied. This is a physical problem, but since it is difficult to find phenomena in nature where the scale of the shock wave is not small compared to the scale of the reaction it has its greatest importance in the context of numerical methods. In [8] it is proposed that detonations cannot exist if the pressure is too large. This observation was probably due to numerical difficulties, since for large values of the ambient pressure the solution approaches the ZND detonation in such a way that the width of the shock wave is constant whereas the width of the reaction zone tends to infinity. The authors used a shooting method, starting in the vicinity of the burnt state. For large values of the ambient pressure (corresponding to small Kr, see notation below), this method becomes extremely sensitive to the initial, shooting data (this follows from an investigation of the behavior of the solution in the vicinity of the corresponding critical point), and it is easy to "run out of accuracy". This work is continued in [3], where an assumption of ignition kinetics is made. Here it is numerically verified that there exists a value of the rate of reaction above which no detonation is possible. This value corresponds to Kr cr introduced below. For an investigation of the case whe