Work

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

Year: 2025

Type: article

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.

Source: Stochastic Processes and their Applications

DOI: 10.1016/j.spa.2025.104646

Authors: Mario Maurelli, Daniela Morale, Stefania Ugolini

Institutions: University of Pisa, University of Milan

Language: English

Topic: Differential Equations and Boundary Problems

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,520

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", Università degli Studi di Milano, Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni, Science for Equity, Empowerment and Development Division