We study the inverse problem for non-stationary system of magnetic hydrodynamics in which it is required to determine the velocity of the fluid v(x, t), the magnetic tension H(x, t), the pressure gradient ∇p(x, t), but also the external forces f (x) and the current rot j(x). In this case, to the conditions constituting the direct problem are added additional conditions. The trace speed, the magnetic tension, and the pressure gradient in the final moment, time t = T, are taken as additional information. The strong generalized solvability of the inverse problem in the two-dimensional case is proved.
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