Stability of Plane Shock Waves

A new argument is presented that yields the following criterion for plane shocks to be stable: -1<j²(dv/dp)H<1, where j²=(p-p₀)(v₀-v) is the slope of the Rayleigh line, and (dv/dp)H is the slope of the Hugoniot curve in the pressure-volume plane. The lower limit is well known and the consequences of its violation are well understood; however, no such degree of understanding has yet been achieved for the upper limit. It seems likely that it bears an important relation to detonation phenomena.