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 problem is proved also optimality system is derived. Finally, the long-time decay properties for the optimal solutions is established. AMS Subject Classifications: 35B40, 35B37, 35Q35, 49J20 Chinese Library Classifications: O175.27
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