Conservation law

Summary

A conservation law is a partial differential equation of the form $u_t + \nabla \cdot F(u) = 0$. It says that the amount of $u$ in a region changes only by the flux $F(u)$ through its boundary. Mass, momentum and energy in continuum mechanics obey such laws. Nonlinear conservation laws develop discontinuities in finite time, so their theory is built on weak solutions, shock waves and entropy conditions. See the definition.