Branching process representation for nonlinear first-order conservation PDEs in 1D

Abstract

We show that a large class of 1D first-order conservation PDEs can be probabilistically represented using multi-type branching processes. The representation holds when the initial conditions are linear combinations of negative exponentials. We also show that in some cases, the time of gradient blow up can be identified by studying criticality conditions of the corresponding branching processes.

Paper significantly restructured. Results have been generalized further from first version