Robin-type boundary control problems for the nonlinear Boussinesq type equations

Aziz Belmiloudi (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

In this paper, we study a linear and a nonlinear boundary control problems arising from viscous flows. The equations are of nonlinear Navier-Stokes type for the velocity and pressure, of transport-diffusion type for the temperature and the salinity. The essential difficulties are due to the nonlinear nature of a part of the boundary conditions and to the nature of the equations: time-dependent, coupled and nonlinear. The existence and the conditions of the uniqueness of the solution, for the variational problem, are studied. The control is of linear or nonlinear Robin-type and acts on a part of the boundary during a time View the MathML source. The cost function measures the distance between the observed and the computed vorticity. The existence of an optimal control in the admissible set of states and controls is proved. A first order necessary conditions of optimality are obtained.

Mots clés: Optimal control; Robin-type control; Boussinesq type equations; Oceanography

Domaines: Analyse numérique [math.NA]; Optimisation et contrôle [math.OC]; Mécanique des fluides [physics.class-ph]; Mécanique des fluides [physics.class-ph]

Aziz Belmiloudi. Robin-type boundary control problems for the nonlinear Boussinesq type equations. Journal of Mathematical Analysis and Applications, 2002, Volume 273 (Issue 2), pp.428-456. ⟨10.1016/S0022-247X(02)00252-4⟩. ⟨hal-00648922⟩