| Title:
|
Optimal control for $n\times n$ coupled systems governed by Petrowsky type equations with control-constrained and infinite number of variables (English) |
| Author:
|
El-Saify, Hussain A. |
| Author:
|
Bahaa, G. M. |
| Language:
|
English |
| Journal:
|
Mathematica Slovaca |
| ISSN:
|
0139-9918 |
| Volume:
|
53 |
| Issue:
|
3 |
| Year:
|
2003 |
| Pages:
|
291-311 |
| . |
| Category:
|
math |
| . |
| MSC:
|
35R15 |
| MSC:
|
49K20 |
| idZBL:
|
Zbl 1088.49023 |
| idMR:
|
MR2025024 |
| . |
| Date available:
|
2009-09-25T14:15:03Z |
| Last updated:
|
2012-08-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/136886 |
| . |
| Reference:
|
[1] BAHAA G. M.: Quadratic Pareto optimal control of parabolic equation with state-control constraints and an infinite number of variables.IMA J. Math. Control Infoгm. 20 (2003), 167-178. Zbl 1029.49023, MR 1987533 |
| Reference:
|
[2] BEREZANSKII, JU. M.: Self-Adjoint Operators in Spaces of Functions of Infinitely Many Variables.Transl. Math. Monographs 63, Amer. Math. Soc, Providence, RI, 1986. |
| Reference:
|
[3] BEREZANSKII, JU. M.: Self-adjointness of elliptic operator with an infinite number of variables.Ukrain. Mat. Zh. 27 (1975), 729-742. MR 0405094 |
| Reference:
|
[4] EL-SAIFY H. A.: Boundary control for the hyperbolic operator with an infinite number of variables.J. Inst. Math. Comput. Sci. Comput. Sci. Ser. 1 (1990), 47-51. |
| Reference:
|
[5] EL-SAIFY H. A.: Boundary control problem with an infinite number of variables.Internal J. Math. Math. Sci. 28 (2001), 57-62. Zbl 0999.49003, MR 1882683 |
| Reference:
|
[6] EL-SAIFY H. A.-BAHAA G. M.: Optimal control for nxn systems of hyperbolic types.Rev. Mat. Apl. 22 (2001), 41-58. MR 1890942 |
| Reference:
|
[7] EL-SAIFY H. A.-SERAG H. M.-BAHAA G. M.: On optimal control for nxn elliptic system involving operators with an infinite number of variables.A.M.S.E. Advances in Modeling & Analysis 1-A 37 (2000), 47-61. |
| Reference:
|
[8] GALI I. M.-EL-SAIFY H. A.: Optimal control of a system governed by hyperbolic operator with an infinite number of variables.J. Math. Anal. Appl. 85 (1982), 24-30. Zbl 0563.49013, MR 0647556 |
| Reference:
|
[9] GALI I. M.-EL-SAIFY H. A.: Distributed control of a system governed by Dirichlet and Neumann Problems for a self-adjoint elliptic operator with an infinite number of variables.J. Optim. Theory Appl. 39 (1983), 293-298. Zbl 0481.49015, MR 0693688 |
| Reference:
|
[10] IMANUVILOV O. YU.: On exact controllability for the Navier-Stokes equations.ESAIM: Control. Optim. Calc. Var. 3 (1998), 97-131. Zbl 1052.93502, MR 1617825 |
| Reference:
|
[11] KOTARSKI W.: Optimal control of a system governed by Petrowsky type equation with an infinite number of variables.Acta Univ. Palack. Olomuc. Fac. Rerum Natur. Math. 35 (1996), 73-82. Zbl 0961.49011, MR 1485046 |
| Reference:
|
[12] KOTARSKI W.-EL-SAIFY H. A.-BAHAA G. M.: Optimal control of parabolic equation with an infinite number of variables for non-standard functional and time delay.IMA J. Math. Control Inform. 19 (2002), 461-476. Zbl 1044.49018, MR 1949014 |
| Reference:
|
[13] KOTARSKI W.-EL-SAIFY H. A.-BAHAA G. M.: Optimal control problem for a hyperbolic system with mixed control-state constraints involving operator of infinite order.Internat. J. Pure Appl. Math. 1 (2002), 241-254. Zbl 1009.49021, MR 1912680 |
| Reference:
|
[14] LI X.-YONG J.: Optimal Control Theory for Infinite Dimensional Systems.Birkhauser, Boston, 1995. MR 1312364 |
| Reference:
|
[15] LIONS J. L.: Optimal Control of Systems Governed by Partial Differential Equations.Grundlehren Math. Wiss. 170, Springer-Verlag, Berlin-Heidelberg-New York, 1971. Zbl 0203.09001, MR 0271512 |
| Reference:
|
[16] LIONS J. L.-ENRIQUE Z.: Approximate controllability of a hydro-elastic coupled system.ESAIM: Control. Optim. Calc. Var. 1 (1995), 1-15. Zbl 0878.93034, MR 1382513 |
| Reference:
|
[17] LIONS J. L.-MAGENES E.: Non-Homogeneous Boundary Value Problem and Applications.Vol. I. Grundlehren Math. Wiss. 181, Springer-Verlag, Berlin-Heidelberg-New York, 1972. MR 0350177 |
| . |
