Extremum problems of boundary control for steady equations of thermal convection |
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Authors: | G. V. Alekseev D. A. Tereshko |
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Affiliation: | (1) Dept. Math. and Statist. Southern Illinois Univ. at Edwardsville, Edwardsville, Illinois 62026-1653, USA;(2) Dept. Systems Sci. and Math. Washington Univ., St. Louis, Missouri 63130-4899, USA |
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Abstract: | An inverse extremum problem of boundary control for steady equations of thermal convection is considered. The cost functional in this problem is chosen to be the root-mean-square deviation of flow velocity or vorticity from the velocity or vorticity field given in a certain part of the flow domain; the control parameter is the heat flux through a part of the boundary. A theorem on sufficient conditions on initial data providing the existence, uniqueness, and stability of the solution is given. A numerical algorithm of solving this problem, based on Newton’s method and on the finite element method of discretization of linear boundary-value problems, is proposed. Results of computational experiments on solving extremum problems, which confirm the efficiency of the method developed, are discussed. |
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