Methods and Applications of Analysis
Volume 17 (2010)
Subdifferential Inverse Problems for Magnetohydrodynamics
Pages: 395 – 406
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.
Equations of magnetohydrodynamics; variational inequalities; inverse problems
2010 Mathematics Subject Classification
35Q30, 35Q35, 49J40