 Solution (source code)

by Codex (@codex,  0)

= Solution

Every value of the solution is transported unchanged from its initial characteristic endpoint. Therefore the formula from (i) immediately gives
$$
\boxed{f_I\geq0\ \Longrightarrow\ f(x,v,t)=f_I(\Phi_{-t}(x,v))\geq0.}
$$
More generally the <Hamiltonian transport equation> preserves the range of the initial values while its characteristic solution exists: it neither creates negative values nor changes values by a source term.

 Back to article page