Insensitizing controls for a large-scale ocean circulation model. (English. Abridged French version) Zbl 1029.93035
A linear quasi-geostrophic ocean model is considered. The authors look for controls insensitizing an observation function of the state. The existence of such controls is equivalent to a null controllability property of a cascade Stokes-like system. Under reasonable assumptions on the spatial domains, where the observation and control are performed, they should be able to prove these properties.
Reviewer: Z.Dżygadło (Warszawa)
MSC:
| 93C20 | Control/observation systems governed by partial differential equations |
| 86A05 | Hydrology, hydrography, oceanography |
| 93B05 | Controllability |
| 76D07 | Stokes and related (Oseen, etc.) flows |
| 76E20 | Stability and instability of geophysical and astrophysical flows |
| 93C05 | Linear systems in control theory |
Keywords:
quasi-geostrophic ocean model; circulation flow; control insensitizing to an observation function of stateReferences:
| [1] | Bodart, O.; Fabre, C., Controls insensitizing the norm of the solution of a semilinear heat equation, J. Math. Anal. Appl., 195, 658-683 (1995) · Zbl 0852.35070 |
| [2] | Bodart, O.; González-Burgos, M.; Pérez-Garcı́a, R., Insensitizing controls for a semilinear heat equation with a superlinear nonlinearity, C. R. Acad. Sci. Paris, Ser. I, 335, 677-682 (2002) · Zbl 1021.35049 |
| [3] | Fabre, C., Uniqueness results for Stokes equations and their consequences in linear and nonlinear control problems, ESAIM: Control Optim. Calc. Var., 1, 267-302 (1996) · Zbl 0872.93039 |
| [4] | Fabre, C.; Lebeau, G., Régularité et unicité pour le problème de Stokes, Comm. Partial Differential Equations, 27, 437-475 (2002) · Zbl 1090.35143 |
| [5] | E. Fernández-Cara, S. Guerrero, O.Y. Imanuvilov, J.-P. Local null controllability of the Navier-Stokes system, in press; E. Fernández-Cara, S. Guerrero, O.Y. Imanuvilov, J.-P. Local null controllability of the Navier-Stokes system, in press · Zbl 1267.93020 |
| [6] | Fursikov, V. A.; Imanuvilov, O. Y., Controllability of Evolution Equations, Lecture Notes (1996), Research Institute of Mathematics, Seoul National University: Research Institute of Mathematics, Seoul National University Korea · Zbl 0862.49004 |
| [7] | Imanuvilov, O. Y., Remarks on the controllability of Navier-Stokes equations, ESAIM: Control Optim. Calc. Var., 6, 39-72 (2001) · Zbl 0961.35104 |
| [8] | Lions, J.-L., Quelques notions dans l’analyse et le contrôle de systèmes à données incomplètes, (Proceedings of the XIth Congress on Differential Equations and Applications First Congress on Applied Mathematics, Málaga, Spain (1990)), 43-54 |
| [9] | Marchuk, G. I.; Agoshkov, V. I.; Shutyaev, V. P., Adjoint Equations and Perturbation Algorithms in Nonlinear Problems (1996), CRC Press: CRC Press Boca Raton, FL · Zbl 1435.65008 |
| [10] | Myers, P. G.; Weaver, A. J., A diagnostic barotropic finite-element ocean circulation model, J. Atmos. Ocean Tech., 12, 511-526 (1995) |
| [11] | Temam, R., Navier-Stokes Equations (1984), North-Holland: North-Holland Amsterdam · Zbl 0572.35083 |
| [12] | De Teresa, L., Insensitizing control for a semilinear heat equation, Comm. Partial Differential Equations, 25, 1/2, 39-72 (2000) · Zbl 0942.35028 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
