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

TL;DR

This paper introduces a probabilistic framework for a complex reaction-advection-diffusion system modeling sulphation, using non-Markovian stochastic equations to interpret the nonlinear PDE and analyzing the system's well-posedness and particle interactions.

Contribution

It provides a novel probabilistic interpretation of a non-conservative, path-dependent PDE through non-Markovian stochastic differential equations, and studies the system's well-posedness and particle propagation.

Findings

Established well-posedness of the stochastic model

Proved propagation of chaos for the particle system

Linked the PDE with a McKean-Vlasov stochastic process

Abstract

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.