Subdifferential Inverse Problems for Magnetohydrodynamics

The theory of solvability of an abstract evolution inequality in a Hilbert space for the operators with the quadratic nonlinearity is presented. It is then applied for the study of an inverse problem for MHD flows. For the three-dimensional flows the global in time existence of the weak solutions to the inverse problem is proved. For the two-dimensional flows existence and uniqueness of the strong solutions are proved.

Keywords

Equations of magnetohydrodynamics, variational inequalities, inverse problems

2010 Mathematics Subject Classification

35Q30, 35Q35, 49J40

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Published 1 January 2010