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JOURNALS // Sibirskii Zhurnal Industrial'noi Matematiki // Archive

Sib. Zh. Ind. Mat., 2012 Volume 15, Number 4, Pages 3–16 (Mi sjim747)

This article is cited in 4 papers

On the stability of solutions to coefficient inverse extreme problems for the stationary convection-diffusion equation

G. V. Alekseevab, M. A. Shepelovac

a Institute of Applied Mathematics, Far-Eastern Branch of the Russian Academy of Sciences, Vladivostok, Russia
b Vladivostok State University of Economics and Service, Vladivostok, Russia
c Far Eastern Federal University, Vladivostok, Russia

Abstract: We study the coefficient inverse problem for the extreme stationary convection-diffusion, considered in a bounded domain with mixed boundary conditions on the boundary. The role of control is played by the velocity vector of the medium and the functions involved in the boundary conditions for the temperature. The solvability of extremal problems is proved for arbitrary weak lower semicontinuous quality functional as well as for specific quality functionals. On the basis of the analysis of the optimality system, we establish sufficient conditions on the initial data that guarantee the uniqueness and stability of optimal solutions under small perturbations of the quality functional as well as of one of the functions outside the initial boundary value problem.

Keywords: convection-diffusion equation, temperature, velocity vector, multiplicative control, coefficient inverse problems, existence, uniqueness, stability.

UDC: 517.95

Received: 06.08.2012


 English version:
Journal of Applied and Industrial Mathematics, 2013, 7:1, 1–14

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