Controllability of Co-Operative Neumann Parabolic Systems
Pure and Applied Mathematics Journal
Volume 4, Issue 1, February 2015, Pages: 32-38
Received: Jan. 10, 2015; Accepted: Jan. 25, 2015; Published: Feb. 2, 2015
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Mohammed Shehata, Department of Mathematics, Faculty of Science, Jazan University, Jazan, Kingdom of Saudi Arabia
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In this communication, we introduce and study the various controllability problems for Neumann co-operative parabolic linear system involving Laplace operator with distributed or boundary controls and with observations belong to different spaces.
Optimal Control Problem, Controllability, Solutions of Parabolic System, Co-Operative System
To cite this article
Mohammed Shehata, Controllability of Co-Operative Neumann Parabolic Systems, Pure and Applied Mathematics Journal. Vol. 4, No. 1, 2015, pp. 32-38. doi: 10.11648/j.pamj.20150401.15
D.L. Russell, Controllability and stabilizability theory for linear partial differential equations. Recent progress and open questions, SIAM Review 20 (1978), 639-739.
H. T. BANKS, M. Q. JACOBS and R. M. LATINA, The synthesis of optimal controls for linear, time optimal problems with retarded controls, J . Optimization Theory Appl. 8 (1971), 319—360.
J.L.Lions, "Remarks on approximate controllability, J. Anal. Math, 59, (1992),103-116..
M. C. DELFOUR and S. K. MITTER, Controllability and observability for infinite- dimensional systems, SIAM J. Control Optim. 10 (1972), 329—333.
H. O. FATTORINI, Some remarks on complete montrollability, SIAM J. Control Optim. 4 (1966), 686—694.
H. O. FATTORINI, Boundary control of temperature distributions in a parallelepipedan, SIAM J. Control Optim. 13 (1975), 1—13.
H. O. FATTORINI and D. L. RUSSELL, Exact controllability theorems for linear parabolitic equations in one space dimension, Arch. Rational Mech. Anal. 43 (1971), 272—292.
J. KLAMKA, Controllability of linear systems with time-variable delays in control, Informat. J . Control 24 (1976), 869—878.
J. KLAMKA, Absolute controllability of linear systems with time-variable delays in control, Systems Sci. 4 (1978), 43—52.
J. JLLAMKA, Relative controllability of infinite-dimensional systems w ith delays in control, Systems Sci. 4 (1978)) 43—52.
A. W. OLBROT, On the controllability of linear systems with time delays in control, IEEE Trans. Automat. Control 17 (1972), 664—666.
D. L. RUSSELL, A unified boundary controllability theory for hyperbolic and parabolic partial differential equations, Studies in Appl. Math. 52 (1973), 189— 211.
Y. SAKAWA, Controllability for partial differential equations of parabolic type, SIAM J. Control Optim. 12 (1974), 389—400.
T. I. SEIDMAN, Observation and prediction for the heat equation. IV: Patch observability and controllability, SIAM J. Control Optim. 15 (1977), 412—427.
G. Knowles Time optimal control of parabolic systems with boundary condition involving time delays, Journal of Optimiz.Theor. Applics, 25,( 1978), 563-574 .
R. TRIGGIANI, Controllability and observability in Banach space with bounded operators, SIAM J. Control Optim. 13 (1975), 462—491.
R. TRIGGIANI, Extensions of rank conditions for controllability and observability to Banach space and unbounded operators, SIAM J. Control Optim. 14 (1976), 313—338.
R. TRIGGIANI, On the lack of exact controllability for mild solutions in Banach space, J. Math. Anal. Appl. 50 (1975), 438—446.
J.-L. Lions, Exact controllability, stabilizability and perturbations for distributed systems, SIAM Review, 30 (1988), 1-68.
J.L.Lions, Optimal control of systems governed by partial differential equations, Springer-verlag, Band 170, (1971).
J.L.Lions and E.Magenes, " Non homogeneous boundary value problem and applications, I, II, Spring-Verlage, New York, (1972).
H. O. Fattorini, Infinite dimensional Optimization Theory and Opotimal Control, Cambridge Univ. Prees (1998).
H.A. El-Saify, H.M. Serag and M.A.Shehata, Time-optimal control for co-operative hyperbolic systems Involving Laplace operator. Journal of Dynamical and Control systems.15,3,(2009),405-423.
M.A.Shehata, Some time-optimal control problems for co-operative hyperbolic systems with distributed or boundary controls. Journal of Mathematical Sciences: Advances and Applications. vol 18, No 1-2,(2012),63-83.
M.A.Shehata, Time -optimal control problem for co-operative parabolic systems with control in initial conditions, Advances in Pure Mathematics Journal , 3, No 9A,(2013),38-43.
M.A.Shehata, Dirichlet Time-Optimal Control of Co-operative Hyperbolic Systems Advanced Modeling and Optimization Journal. Volume 16, Number 2, (2014),355-369.
Byung Soo Lee, Mohammed Shehata, Salahuddin , Time -optimal control problem for co-operative parabolic systems with strong constraint control in initial conditions, Journal of Science and Technology, Vol.4 No.11,(2014)..
R.A. Adams, Sobolev Spaces, Academic Prees, New York, (1975).
J. Fleckinger, J. Hern ndez and F.DE. Th lin, On the existence of multiple principal eigenvalues for some indefinite linear eigenvalue problems, Rev.R.Acad.Cien.Serie A.Mat. 97,2 (2003), 461-466.
H. Tanabe, On differentiability and analyticity of eighted elliptic boundary value problems, Osaka Math.Journal ,2 (1965),163-190.
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