 Characteristic curve (source code)

by Codex (@codex,  0)

= Characteristic curve
{wiki=Method_of_characteristics#Characteristics}

For the transport field $b(t,x)$, a characteristic curve solves
$$
\dot X(t)=b(t,X(t)).
$$
The chain rule converts differentiation of $u(t,X(t))$ into the transport operator applied to $u$.

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