Coefficient identification problems for a steady-state mass-transfer model in the Oberbeck-Boussinesq approximation are considered. Optimality systems describing necessary conditions for the existence of an extremum are obtained, and, by analysis of their properties, conditions ensuring the uniqueness and stability of the solution are established.Introduction. In recent years, the need to determine effective mechanisms for controlling thermodynamic processes in viscous liquids has led to considerable attention being focused on optimal control problems for heatand mass-transfer models. Theoretical investigation of the indicated problems has been the subject of a considerable number of papers (see, for example, [1][2][3][4]).Along with optimal control problems, of great significance are identification problems for heat-and masstransfer models, i.e., the determination (using additional information on the state of the medium) of the unknown densities of the boundary or distributed sources or the coefficients included in the differential equations or boundary conditions of the examined model. It should be noted that the solution of identification problems reduces to studying corresponding extremum problems with an adequate choice of the minimized quality functional. This allows control problems and identification problems to be investigated in terms of the theory of extremum problems of conditional optimization in Hilbert spaces.Extremum problems of finding the source density have been studied in a number of papers (see, for example, [5-7]); less attention has been given to coefficient identification problems. We only note a paper [8], which, along with identification problems for source density, considers the problem of identification of the boundary condition coefficient for a thermal convection model.1. Formulation of the Basic Boundary-Value Problem. The purpose of the present work is to study identification problems for the following mass transfer model:

Abstract. Two approaches (direct design and inverse design methods) for solving problems of designing devices providing invisibility of material bodies of detection using different physical fields -electromagnetic, acoustic and static are discussed. The second method is applied for solving problems of designing cloaking devices for the 3D stationary thermal scattering model. Based on this method the design problems under study are reduced to respective control problems. The material parameters (radial and tangential heat conductivities) of the inhomogeneous anisotropic medium filling the thermal cloak and the density of auxiliary heat sources play the role of controls. A unique solvability of direct thermal scattering problem in the Sobolev space is proved and the new estimates of solutions are established. Using these results, the solvability of control problem is proved and the optimality system is derived. Based on analysis of optimality system, the stability estimates of optimal solutions are established and numerical algorithms for solving particular thermal cloaking problem are proposed.

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The article shows the response of barley seeds to the influence of an electromagnetic field of ultrahigh frequency (EMF microwave). The action of microwave EMF leads to a change in the qualitative and quantitative composition of fatty acids contained in the organs of barley seedlings. The main saturated fatty acids that make up barley seed lipids are palmitic, and among unsaturated ones are oleic and linolenic acids. The content of other higher aliphatic acids is low. The maximum changes under the influence of microwave EMF occur in the sprouts and roots of seedlings with an increase in the number of carbon atoms in the fatty acid molecule. The most important for the growth and development of leaves is saturated hexacosan fatty acid with 26 carbon atoms, for roots unsaturated aceterucic C24:1, for endospermsaturated tricocylic acid with an odd number of carbon atoms (C23:0). Synthesis of long-chain fatty acids plays an important role in cell growth. Changes in the content of such compounds affect the development of embryos, leaves, and roots. Long-chain fatty acids are involved in regulating cell size, cell division, and cell differentiation.

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