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On the controllability of diffusion processes on a sphere: a numerical study. (English) Zbl 1353.49042

Summary: The main goal of this article is to study computationally the controllability of a diffusion process on the surface of a sphere in \(\mathbb{R}^3\). 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.

MSC:

49M25 Discrete approximations in optimal control
93B05 Controllability
49K20 Optimality conditions for problems involving partial differential equations
65K10 Numerical optimization and variational techniques
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
93C20 Control/observation systems governed by partial differential equations
58E25 Applications of variational problems to control theory
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