Abstract
An inverse problem for a nonlinear equation in a Hilbert space is considered in which the right-hand side that is a linear combination of given functionals is found from given values of these functionals on the solution. Sufficient conditions for the existence of a solution are established, and the solution set is shown to be homeomorphic to a finite-dimensional compact set. A boundary inverse problem for the three-dimensional thermal convection equations for a viscous incompressible fluid and an inverse magnetohydrodynamics problem are considered as applications.
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Original Russian Text © A.Yu. Chebotarev, 2014, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2014, Vol. 54, No. 3, pp. 519–528.
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Chebotarev, A.Y. Inverse problems for stationary Navier-Stokes systems. Comput. Math. and Math. Phys. 54, 537–545 (2014). https://doi.org/10.1134/S0965542514030038
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DOI: https://doi.org/10.1134/S0965542514030038