Stability of Plane Shock Waves

A new argument is presented that yields the following criterion for plane shocks to be stable: $-1<j^2{\left(\frac{\mathrm{dv}}{\mathrm{dp}}\right)}_{\mathrm{H}}<1\mathrm{}$, where $j^2=\frac{(p-p_0)}{(v_0-v)}$ is the slope of the Rayleigh line, and ${\left(\frac{\mathrm{dv}}{\mathrm{dp}}\right)}_{\mathrm{H}}$ 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.