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 in the description of the evolution of the chemical reaction of sulphur dioxide with the surface of calcium carbonate stones. The boundary condition is given by a Jacobi process, solution to a Brownian motion-driven 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.
Well-posedness of a reaction-diffusion model with stochastic dynamical boundary conditions / M. Maurelli, D. Morale, S. Ugolini. - (2023 Aug 13).
Well-posedness of a reaction-diffusion model with stochastic dynamical boundary conditions
M. Maurelli;D. Morale;S. Ugolini
2023
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 in the description of the evolution of the chemical reaction of sulphur dioxide with the surface of calcium carbonate stones. The boundary condition is given by a Jacobi process, solution to a Brownian motion-driven 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.File | Dimensione | Formato | |
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