TY - JOUR
T1 - On the controllability of diffusion processes on a sphere
T2 - A numerical study
AU - Velasco, D. Assaely León
AU - GLOWINSKI, Roland
AU - Valencia, L. Héctor Juárez
N1 - Funding Information:
The authors want to acknowledge the financial support from CONACYT (National Council of Science and Technology in Mexico) through a scholarship for the first author, who did a one-year internship at the University of Houston under the supervision of the second author, and also for the support of the network research group Red de Matematicas y Desarrollo. We acknowledge also the support from the Math Graduate program at Universidad Aut?noma Metropolitana, from the Institute for Advanced Studies at the Hong Kong University of Sciences and Technology, and from the Department of Mathematics at the Hong-Kong Baptist University.
PY - 2016
Y1 - 2016
N2 - 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.
AB - 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.
KW - Approximate controllability
KW - Conjugate gradient
KW - Diffusion process
KW - Laplace-Beltrami operator
KW - Null-controlability
KW - Surface of a shere
UR - http://www.scopus.com/inward/record.url?scp=84981210876&partnerID=8YFLogxK
U2 - 10.1051/cocv/2016045
DO - 10.1051/cocv/2016045
M3 - Journal article
AN - SCOPUS:84981210876
SN - 1292-8119
VL - 13
JO - ESAIM - Control, Optimisation and Calculus of Variations
JF - ESAIM - Control, Optimisation and Calculus of Variations
ER -