We study the dynamics of a piecewise （in time） distributed optimal con- trol problem for Generalized MHD equations which model velocity tracking coupled to magnetic field over time. The long-time behavior of solutio...We study the dynamics of a piecewise （in time） distributed optimal con- trol problem for Generalized MHD equations which model velocity tracking coupled to magnetic field over time. The long-time behavior of solutions for an optimal dis- tributed 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 prelimi- nary estimates for the long-time behavior of all solutions of Generalized MHD equa- tions 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 opti- mal solutions is established.展开更多
文摘We study the dynamics of a piecewise （in time） distributed optimal con- trol problem for Generalized MHD equations which model velocity tracking coupled to magnetic field over time. The long-time behavior of solutions for an optimal dis- tributed 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 prelimi- nary estimates for the long-time behavior of all solutions of Generalized MHD equa- tions 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 opti- mal solutions is established.
