Resumen
Abstract We 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. Piecewise deterministic evolutions - Stochastic optimal control - Logarithmic transformation - Nonlinear field equations