On the controllability of diffusion processes on a sphere: A numerical study
1 Departamento de Matemáticas, Universidad Autónoma Metropolitana Unidad Iztapalapa, Av. San Rafael Atlixco 186, Col. Vicentina, D.F. 09340, Mexico.
2 Deparment of Mathematics, University of Houston, 4800 Calhoun, Houston, TX 77004, USA.
3 Baptist University, Hong-Kong, P.R. China.
Received: 6 June 2016
Accepted: 7 June 2016
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.
Mathematics Subject Classification: 49K20 / 58E25 / 65K10 / 65M60 / 93M05 / 93C20
Key words: Diffusion process / surface of a shere / conjugate gradient / null-controlability / approximate controllability / Laplace−Beltrami operator
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