System of conservation laws
= System of conservation laws
{title2=$U_t+\partial_xF(U)=0$}
A system of conservation laws evolves a vector of conserved variables $U$ through a flux vector $F(U)$. For a smooth solution it has quasilinear form $U_t+A(U)U_x=0$, where $A(U)=DF(U)$ is the <flux Jacobian>.