Geodesic
Investigation of boundary control and final observation in mathematical model of motion speed potentials distribution of filtered liquid free surface
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 16 (2023) no. 2, pp. 111-116 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper, we study the problem of boundary control and final observation for one degenerate mathematical model of motion speed potentials distribution of filtered liquid free surface with the Showalter–Sidorov initial condition. The mathematical model is based on the degenerate Boussinesq equation with an inhomogeneous Dirichlet condition. This model belongs to the class of semilinear Sobolev-type models in which the nonlinear operator is $p$-coercive and $s$-monotone. In the paper, the problem of boundary control and final observation for a semilinear Sobolev-type model is considered and conditions for the existence of a control-state pair of the problem are found. In applied studies of a research problem, it is allowed to find such a potentials distributionof filtered liquid free surface, at which the system transitions from the initial condition to a given final state within a certain period of time $T$.
Keywords: mathematical model of motion speed potentials distribution of filtered liquid free surface, problem of boundary control and final observation, the Sobolev type equations. 
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     title = {Investigation of boundary control and final observation in mathematical model of motion speed potentials distribution of filtered liquid free surface},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
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K. V. Perevozchikova; N. A. Manakova. Investigation of boundary control and final observation in mathematical model of motion speed potentials distribution of filtered liquid free surface. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 16 (2023) no. 2, pp. 111-116. http://geodesic.mathdoc.fr/item/VYURU_2023_16_2_a10/

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