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Optimality of Distributed Control for <i>n × n</i> Hyperbolic Systems with an Infinite Number of Variables
Department of Mathematics, Faculty of Applied sciences, Umm AL-Qura University, Makkah, Saudi Arabia
- 1 Department of Mathematics, Faculty of Applied sciences, Umm AL-Qura University, Makkah, Saudi Arabia
Advances in Pure Mathematics·Volume 03 (2013)·Pages 598–608·Published 29 August 2013·DOI10.4236/apm.2013.36077
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Abstract
In this paper, we study the existence of solutions for 2 l order ( n × n ) cooperative systems governed by Dirichlet and Neumann problems involving hyperbolic operators with an infinite number of variables and with variable coefficients. The necessary and sufficient conditions for optimality of the distributed control with constraints are obtained and the set of inequalities that defining the optimal control of these systems are also obtained.
KeywordsHyperbolic OperatorsCooperative SystemsSpaces With an Infinite Number of VariablesExistence and Uniqueness of SolutionsDistributed Control ProblemsControl ConstraintsVariable Coefficients
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