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- W1976642744 abstract "In this paper we present a method of optimal control developed in order tocalculate the current corresponding to the observed sea level in a fluid domain $Omega$ and during a time T. The control is the external stress $f $. The cost function measures the distance between the observed and computed sea levels. The equations satisfied by the depth and the depth averaged velocity are of nonlinear shallow-water type. The existence and uniqueness of a solution for the direct problem are studied in the case of Dirichlet nonhomogeneous boundary conditions. We prove, by means of minimizing sequences, the existence of an optimal control $(f ,U )$ in the case of the small data and a very viscous fluid. To characterize it we build a sequence of problems corresponding to a linearization of the direct problem. We obtain the necessary conditions of optimality. The set of equations and the inequality characterizing the optimal control $(f ,U )$ is obtained as the limit of the penalization." @default.
- W1976642744 created "2016-06-24" @default.
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- W1976642744 date "2000-01-01" @default.
- W1976642744 modified "2023-09-23" @default.
- W1976642744 title "Existence and Characterization of an Optimal Control for the Problem of Long Waves in a Shallow-Water Model" @default.
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- W1976642744 doi "https://doi.org/10.1137/s0363012999335961" @default.
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