Distributed control for cooperative Parabolic systems with conjugation conditions

H. M. Serag; S. A. El-Zahaby; L. M. Abd-Elrahman

H. M. Serag Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr City (11884), Cairo, Egypt
S. A. El-Zahaby Department of Mathematics, Faculty of Science, Al-Azhar University [For Girls], Nasr City, Cairo, Egypt
L. M. Abd-Elrahman Department of Mathematics, Faculty of Science, Al-Azhar University [For Girls], Nasr City, Cairo, Egypt

Keywords: Distributed control, existence of solution, Cooperative Parabolic Systems, Conjugation Conditions, Dirichlet and Neumann Conditions, Laplace Operator, Case without Constraints.

Abstract

In this paper, we consider cooperative Parabolic systems defined on bounded, continuous and strictly Lipschitz domain of Rⁿwith conjugation conditions. We study the optimal control for these systems with Dirichlet conditions. Also ,we establish the problem with Neumann conditions .The control in our problems is of distributed type .

Downloads

Download data is not yet available.

References

El-Saify, H. A. , Serag , H. M. and Shehata,M.A. ,Time optimal control problem for cooperative hyperbolic systems involving the Laplace operator,Journal of Dynamics and Control Systems, Vol.15, No. 3, (2009), pp. 405-423.

Fleckinger J., and Serag, H. M. , Semilinear cooperative elliptic systems on Rn , Rend. Mat. Appl., Vol. 15 , No.1, (1995), pp.

-108.

Gali, I. M and EL-Saify H. A. , Distributed control of a system governed by Dirichlet and Neumann problems for a self adjoint

elliptic operator with an in finite number of Variables, J. of Optimization Theory an Applications,Vol.39. No.2,(1983), pp. 293-298.

Gali, I.M and EL-Saify H.A and El-Zahaby,S.A., Distributed control of a system governed by Dirichlet and Neumann problems for elliptic equations of infinite order, Proc. Int. Conf. Of Functional Diff. Systems and Related Topics III, Poland, (1983), pp.83-87.

Gali, I.M. and Serag,H.M. , Optimal control of cooperative elliptic systems defined on Rn,J. of the Egyptian Mathematical Society,

Vol. 3,(1995), pp.33-39.

Lions,J.L., Optimal control of a system governed by partial differential equations, Springer -Verlag, New York 170,(1971).

Lions,J.L., Some methods in the Mathematical analysis of systems and their control ,Science Press,Beijing,1981.

Serag,H. M., Optimal control of cooperative elliptic system on Rn, J. of the Egyptian Mathematical Society, Vol.3,(1995), pp.33-39.

Serag,H. M., Optimal control of systems involving Schrodinger operators,Int. J. of Control and Intelligent Systems ,Canada ,

Vol.32, No.3 (2004), pp.154-159.

Serag,H. M.and Qamlo,A .H., On elliptic systems involving Schrodinger operator, The Mediterranean J. of Measurement and

Control, Vol.1, No.2,(2005), pp.91-96.

Serag, H. M., Distributed control for cooperative systems involving Parabolic operators with an infinite number of variables, IMA J. of Mathematical Control and Information,Vol.24 , No.2, (2007), pp. 149-161.

Serag, H. M. and Khafagy, S., On non homogeneous n × n elliptic systems involving p- Laplacian with different weights, J. of Advanced Research in Differential Equations, Vol.33, (2009), pp.1-13.

Serag, H. M. and Elsaban, A.A.,Boundary control for cooperative elliptic systems with conjugation conditions Accepted for publication in J.Advances in Diff.Eqns.and control Processes,2014.

Sergienko I.V.and Deineka V.S. , Optimal control of an elliptic -parabolic system with conjugation conditions , Cybernetics and

Systems Analysis, Vol.39, No.3,(2003), pp. 402-418.

Sergienko I.V. and Deineka V. S, Optimal control of an elliptic system with conjugation conditions and Neumann boundary conditions, Cybernetics and Systems Analaysis, Vol. 40, No. 6,(2004), pp.865-882.

Sergienko I. V. and Deineka V. S, Optimal control of distributed systems with conjugation conditions, Springer (2005).

Qamlo,A. H., Distributed control for cooperative hyperbolic systems involving Schrodinger operator, International Journal of Dynamics and control , (2013), pp.54-59.

Qamlo,A. H., optimality conditions for Parabolic systems with variable coefficients involving Schrodinger operators , Journal of King Saud University -Science ,(2013).