  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.
