Volume 26, Issue 1
Dynamics for Controlled 2D Generalized MHD Systems with Distributed Controls

De G. Akmel and L. C. Bahi

10.4208/jpde.v26.n1.5

J. Part. Diff. Eq., 26 (2013), pp. 48-75.

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  • Abstract

We study the dynamics of a piecewise (in time) distributed optimal control problem for Generalized MHD equations which model velocity tracking coupled to magnetic field over time. The long-time behavior of solutions for an optimal distributed control problem associated with the Generalized MHD equations is studied. First, a quasi-optimal solution for the Generalized MHD equations is constructed; this quasi-optimal solution possesses the decay (in time) properties. Then, some preliminary estimates for the long-time behavior of all solutions of Generalized MHD equations are derived. Next, the existence of a solution of optimal control problemis proved also optimality system is derived. Finally, the long-time decay properties for the optimal solutions is established.

  • History

Published online: 2013-03

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