Department of Mathematics2024-11-0920040095-461610.1007/s00245-003-0786-22-s2.0-21144431574http://dx.doi.org/10.1007/s00245-003-0786-2https://hdl.handle.net/20.500.14288/8418We construct the explicit connection existing between a solvable model of the discrete velocities non-linear Boltzmann equation and the Hamilton-Bellman-Jacobi equation associated with a simple optimal control of a piecewise deterministic process. This study extends the known relation that exists between the Burgers equation and a simple controlled diffusion problem. In both cases the resulting partial differential equations can be linearized via a logarithmic transformation and hence offer the possibility to solve physically relevant non-linear field models in full generality.MathematicsJournal Article189001800002Q27922