A probabilistic interpretation of a non-conservative and path-dependent nonlinear reaction-advection-diffusion system

Given a reaction-advection-diffusion system modelling the sulphation phenomenon, we derive a single regularised non-conservative and path-dependent nonlinear partial differential equation and propose a probabilistic interpretation via a non-Markovian McKean-Vlasov stochastic differential equation coupled with a Feynman-Kac-type equation. We discuss the well-posedness of such a stochastic model, and establish the propagation of chaos property for the associated interacting particle system.