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Zh. Vychisl. Mat. Mat. Fiz., 2012, Volume 52, Number 12, Pages 2190–2205 (Mi zvmmf9809)  

This article is cited in 20 scientific papers (total in 20 papers)

Stability estimates in identification problems for the convection-diffusion-reaction equation

G. V. Alekseeva, I. S. Vakhitovb, O. V. Sobolevab

a Far Eastern Federal University, Vladivostok
b Institute of Applied Mathematics, Far-Eastern Branch of the Russian Academy of Sciences, Vladivostok

Abstract: Identification problems for the stationary convection-diffusion-reaction equation in a bounded domain with a Dirichlet condition imposed on the boundary of the domain are studied. By applying an optimization method, these problems are reduced to inverse extremum problems in which the variable diffusivity and the volume density of substance sources are used as control functions. Their solvability is proved for an arbitrary weakly lower semicontinuous cost functional and particular cost functionals. An analysis of the optimality system is used to establish sufficient conditions on the input data under which the solutions of particular extremum problems are unique and stable with respect to small perturbations in the cost functional and in one of the functions involved in the boundary value problem.

Key words: mass transfer model, convection-diffusion-reaction equation, variable diffusivity, coefficient inverse problems, stability estimates.

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English version:
Computational Mathematics and Mathematical Physics, 2012, 52:12, 1635–1649

Bibliographic databases:

UDC: 519.34
Received: 09.07.2012

Citation: G. V. Alekseev, I. S. Vakhitov, O. V. Soboleva, “Stability estimates in identification problems for the convection-diffusion-reaction equation”, Zh. Vychisl. Mat. Mat. Fiz., 52:12 (2012), 2190–2205; Comput. Math. Math. Phys., 52:12 (2012), 1635–1649

Citation in format AMSBIB
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