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

De G. Akmel & L. C. Bahi

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

Published online: 2013-03

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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.

  • Keywords

Optimal control generalized MHD equations long-time behavior

  • AMS Subject Headings

35B40 35B37 35Q35 49J20

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

akmelde@yahoo.fr (De G. Akmel)

baclemsy@yahoo.fr (L. C. Bahi)

  • BibTex
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  • TXT
@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 = {

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.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v26.n1.5}, url = {http://global-sci.org/intro/article_detail/jpde/5153.html} }
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 -

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.

De G. Akmel & L. C. Bahi. (2019). Dynamics for Controlled 2D Generalized MHD Systems with Distributed Controls. Journal of Partial Differential Equations. 26 (1). 48-75. doi:10.4208/jpde.v26.n1.5
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