Abstract:

We consider a reaction diffusion model on the half line, proposed to describe the marble sulphation process. To better describe the external sulphur dioxide concentration, we introduce a stochastic dynamical boundary condition. This boundary condition is given by a Jacobi process, solution to a stochastic differential equation driven by a Brownian motion. We show global existence and pathwise uniqueness of the reaction diffusion system coupled with the stochastic boundary condition. The proof relies on a splitting strategy, which allows to deal with the low regularity of the boundary condition. Joint work with Daniela Morale and Stefania Ugolini.