Methods and Applications of Analysis

Volume 17 (2010)

Number 4

Subdifferential Inverse Problems for Magnetohydrodynamics

Pages: 395 – 406

DOI: http://dx.doi.org/10.4310/MAA.2010.v17.n4.a5

Author

Alexander Chebotarev

Abstract

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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