Geodesic
Optimal control in the mathematical model of internal waves
Journal of computational and engineering mathematics, Tome 7 (2020) no. 1, pp. 62-71

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The paper presents the results of the study of the problem on the optimal control to solutions for a mathematical model of internal waves, which is based on a linear system of equations of hydrodynamics. This model describes the propagation of waves in a homogeneous incompressible stratified fluid. The mathematical model includes the Sobolev equation, the Cauchy and Dirichlet condition. We use a parallelepiped as a considered domain in the mathematical model. The paper shows existence and uniqueness of a strong solution to the Cauchy–Dirichlet problem for the Sobolev equation. Also, we obtain the sufficient conditions for existence and uniqueness of a solution to the problem on optimal control to such solutions in Hilbert spaces. Proof of existence and uniqueness of a strong solution is based on the theorem for an abstract incomplete inhomogeneous Sobolev type equation of the second order and the theory of relatively p-bounded operators. In this paper, we present the theorem on existence and uniqueness of the optimal control for the problem under study, which is based on the works of J.-L. Lyons.
Keywords: Sobolev type equations, relatively p-bounded operator, strong solution, optimal control. 
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     author = {K. Yu. Kotlovanov and E. V. Bychkov and A. V. Bogomolov},
     title = {Optimal control in the mathematical model of internal waves},
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     pages = {62--71},
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     number = {1},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JCEM_2020_7_1_a4/}
}
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K. Yu. Kotlovanov; E. V. Bychkov; A. V. Bogomolov. Optimal control in the mathematical model of internal waves. Journal of computational and engineering mathematics, Tome 7 (2020) no. 1, pp. 62-71. http://geodesic.mathdoc.fr/item/JCEM_2020_7_1_a4/