Rankine-Hugoniot condition

The equation forcing a shock's speed to equal the jump in flux divided by the jump in the conserved quantity.

The Rankine–Hugoniot condition $\sigma\llbracket u\rrbracket=\llbracket f(u)\rrbracket$ -- equivalently $\sigma=(f(u_R)-f(u_L))/(u_R-u_L)$ -- fixes the speed $\sigma$ of a shock in a conservation law $u_t+f(u)_x=0$ from the values $u_L,u_R$ on either side, so the conserved quantity's total amount is preserved across the discontinuity.