@Article{JPDE-26-48,
author = {Akmel , De G. and Bahi , L. C.},
title = {Dynamics for Controlled 2D Generalized MHD Systems with Distributed Controls},
journal = {Journal of Partial Differential Equations},
year = {2013},
volume = {26},
number = {1},
pages = {48--75},
abstract = {<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>},
issn = {2079-732X},
doi = {https://doi.org/10.4208/jpde.v26.n1.5},
url = {http://global-sci.org/intro/article_detail/jpde/5153.html}
}