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Abstracts

The purpose of the paper is theoretical analysis of inverse extremal problems for the equation of admixture transfer in an incompressible viscous fluid, considered in a bounded domain of two-dimensional or three-dimensional space with piecewise smooth boundary. In strict mathematical formulation these inverse problems consist in finding parameters of unknown admixture sources or the environment.

For solution of these problems we apply the method which is based on its reduction to solving of respective control problems. Therefore the main attention in the paper is paid to study of control problems in which the densities of admixture sources and some coefficients of differential equation under consideration take the role of controls. These control problems are formulated as the minimization problems of certain cost functionals dependent on control and the solutions. As the corresponding cost functionals we take the L2-deviation of the sought concentration field (or velocity field) from the given one, the L2-norm of the concentration (or velocity) field gradient, etc. On the base of methodology of [1-4] their solvability is studied and the optimality systems which describe the necessary conditions of the minimum are deduced and analyzed.

This work was supported by Russian Foundation of Basic Research under grant № 04-01-00136.

The literature

1. G.V. Alekseev, Inverse extremum problems for stationary equations of heat and mass transfer. Dokl. Math. (2000) 62, No. 3, 420 - 424.

2. G.V. Alekseev, Solvability of inverse extremal problems for stationary heat and mass transfer equations. Sib. Math. J. (2001) 42, No. 5, 811 - 827.

3. G.V. Alekseev, Inverse extremal problems for stationary equations in mass transfer theory. Comp. Math. Mathem. Phys. (2002) 42, No. 3, 363 - 376.

4. Alekseev G.V., Prokopenko S.V., Soboleva O.V., Tereshko D.A Optimal control problems for some model of pollution, Vich.tech. 2003. V. 8. Part 4. P. 65-71.

Note. Abstracts are published in author's edition

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