Hongler, MO., Soner, H.M. & Streit, L. Appl Math Optim (2004) 49: 113. doi:10.1007/BF02638147
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