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arXiv:2407.19301 [math.PR]AbstractReferencesReviewsResources

A probabilistic interpretation of a non-conservative and path-dependent nonlinear reaction-diffusion system for the marble sulphation in Cultural Heritage

Daniela Morale, Leonardo Tarquini, Stefania Ugolini

Published 2024-07-27Version 1

Given a reaction-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 using a non-Markovian McKean-type stochastic differential equation. We discuss the well-posedness of such a stochastic model, and we establish the propagation of chaos property for the related interacting particle system.

Categories: math.PR
Subjects: 60H10, 60H30, 60J60, 65C35, 58J35
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