TY - JOUR
T1 - Dynamics for Controlled 2D Generalized MHD Systems with Distributed Controls
AU - Akmel , De G.
AU - Bahi , L. C.
JO - Journal of Partial Differential Equations
VL - 1
SP - 48
EP - 75
PY - 2013
DA - 2013/03
SN - 26
DO - http://doi.org/10.4208/jpde.v26.n1.5
UR - https://global-sci.org/intro/article_detail/jpde/5153.html
KW - Optimal control
KW - generalized MHD equations
KW - long-time behavior
AB - <p>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.</p>