conservation law

A statement that a quantity's rate of change inside a region equals the net rate it flows across that region's boundary, plus any source.

In its differential (pointwise) form, a conservation law for a density $u$ with flux $\phi$ and source $f$ reads $u_t + \nabla\cdot\phi = f$ -- the quantity changes only by flowing in or out (the divergence of $\phi$ ) or by being created or destroyed (by $f$ ).