Geodesic
On the controllability of diffusion processes on a sphere: A numerical study
Assaely León Velasco, D.1 ; Glowinski, Roland2, 3  ; Héctor Juárez Valencia, L.1
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.
ESAIM: Control, Optimisation and Calculus of Variations, Tome 22 (2016) no. 4, pp. 1054-1077

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The main goal of this article is to study computationally the controllability of a diffusion process on the surface of a sphere in R 3 . 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.

Reçu le :
Accepté le :
DOI : 10.1051/cocv/2016045
Classification : 49K20, 58E25, 65K10, 65M60, 93M05, 93C20
Keywords: Diffusion process, surface of a shere, conjugate gradient, null-controlability, approximate controllability, Laplace−Beltrami operator

Assaely León Velasco, D. 1 ; Glowinski, Roland 2, 3 ; Héctor Juárez Valencia, L. 1

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. 
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     title = {On the controllability of diffusion processes on a sphere: {A} numerical study},
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Assaely León Velasco, D.; Glowinski, Roland; Héctor Juárez Valencia, L. On the controllability of diffusion processes on a sphere: A numerical study. ESAIM: Control, Optimisation and Calculus of Variations, Tome 22 (2016) no. 4, pp. 1054-1077. doi: 10.1051/cocv/2016045

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