Well-posedness of a reaction–diffusion model with stochastic dynamical boundary conditions

Mario Maurelli, Daniela Morale and Stefania Ugolini

Stochastic Processes and their Applications, 2025, vol. 186, issue C

Abstract: We study the well-posedness of a nonlinear reaction diffusion partial differential equation system on the half-line coupled with a stochastic dynamical boundary condition, a random system arising from the description of the chemical reaction of sulphur dioxide with calcium carbonate stones. The boundary condition is given by a Jacobi process, solution to a stochastic differential equation with a mean-reverting drift and a bounded diffusion coefficient. The main result is the global existence and the pathwise uniqueness of mild solutions. The proof relies on a splitting strategy, which allows to deal with the low regularity of the dynamical boundary condition.

Keywords: Stochastic dynamical boundary conditions; Nonlinear reaction–diffusion PDEs; Application to sulphation (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1016/j.spa.2025.104646

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