Characteristic equations for a transport equation
= Characteristic equations for a transport equation
{title2=$\dot z=b(t,z),\quad\dot f=h(t,z)$}
For a <transport equation> $\partial_tf+b(t,z)\cdot\nabla_zf=h$, solve $\dot z=b(t,z)$. The <chain rule> then gives $d[f(t,z(t))]/dt=h(t,z(t))$. Initial data and the time <integral> of this source determine the solution along each <characteristic curve>.