Scalar conservation law
= Scalar conservation law
{title2=$u_t+\partial_xf(u)=0$}
{wiki=Conservation_law#One-dimensional_application}
A scalar conservation law in one space dimension has the form $u_t+\partial_xf(u)=0$. While a classical solution exists, it obeys the quasilinear transport equation $u_t+f'(u)u_x=0$.