The relationship between the shock velocity and the particle velocity

It is shown that the linear relationship between the shock velocity and the particle velocity can be obtained as a consequence of the Rankine-Hugoniot equations, if one assumes in addition that for every material there exists a maximum value for the shock compression. The linear relationship results then as a particular solution of a differential equation. It is also shown that the general solution is not linear, but that its asymptotic behavior must be linear.