Optimality Boundary Conditions For Stochastic Elliptic System Involving Higher Order Operator
Volume 2 - Issue 5, May 2018 Edition
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A. M. Abdallah
Optimal Stochastic Control, Optimality conditions, Stochastic analysis
In this present work, we deal with the stochastic elliptic systems where the model of the stochastic elliptic system is higher order operator. We prove the existence and uniqueness of the state variable process of these systems. Then, we give the necessary and sufficient for the optimality of the system.
 A. M. Abdallah “Optimality Conditions for non-cooperative stochastic systems,” Lambert cooperation publishing : Germany, 2018.
 A. M. Abdallah “On Stochastic Elliptic System Involving Higher Order Operator With Dirichlet Conditions,” Journal of AMO - Advanced Modeling and Optimization, vol. 20, no. 1, 2018.
 J. Fleckinger and M. L. Lapidus, “Eigen values of elliptic boundary value problems with an indefinite we weight function,” Transactions of the American Mathematical Society, vol. 295, pp. 305-324, 1986.
 J. L. Lions, Optimal control of a system governed by partial differential equations, Springer-Verlag: New York, 1971.
 A. S. Okb El Bab, Abd-Allah Hyder, and A. M. Abdallah, “Boundary control of stochastic elliptic systems involving Laplace operator,” Journal of AMO - Advanced Modeling and Optimization, vol. 19, pp. 53-61, 2017.
 A. S. Okb El Bab, Abd-Allah Hyder, and A. M. Abdallah, “Distributed control of stochastic elliptic systems involving Laplace operator,” Electronic Journal of Mathematical Analysis and Applications, vol. 5, pp. 191-199, 2017.
 I. V. Sergienko and V. S. Deineka, “Optimal control of an elliptic system with conjugation conditions and Neumann boundary conditions,” Journal of Cyberne-tics and Systems Analysis, vol.40 (2004), pp. 865-882, 2004.