Rankine-Hugoniot condition
= Rankine-Hugoniot condition
{c}
{wiki}
Across a discontinuity $x=\sigma t$ of a <weak solution> to $u_t+f(u)_x=0$, with left and right states $u_-$ and $u_+$, conservation requires
$$
\sigma(u_+-u_-)=f(u_+)-f(u_-).
$$
= Rankine-Hugoniot condition
{c}
{wiki}
Across a discontinuity $x=\sigma t$ of a <weak solution> to $u_t+f(u)_x=0$, with left and right states $u_-$ and $u_+$, conservation requires
$$
\sigma(u_+-u_-)=f(u_+)-f(u_-).
$$