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.
"Subdifferential Inverse Problems for Magnetohydrodynamics." Methods Appl. Anal. 17 (4) 395 - 406, December 2010.