On the controllability of diffusion processes on a sphere: A numerical study

Abstract

The main goal of this article is to study computationally the controllability of a diffusion process on the surface of a sphere in R3 . To achieve this goal, we employ a methodology combining finite differences for the time discretization, finite elements for the space approximation, and a conjugate gradient algorithm for the iterative solution of the discrete control problems. The results of numerical experiments, obtained using the above methodology, will be presented. Furthermore, the null-controllability properties of the diffusion model under consideration will be also studied computationally.