Distributed control of a system governed by Dirichlet and Neumann problems for a self-adjoint elliptic operator with an infinite number of variables

Boundary control problem with an infinite number of variables

“…where A is a bounded selfadjoint elliptic operator of 2 th order with an infinite number of variables which takes the form, [2,4,8,9],…”

“…Using a previous result by Gali and El-Saify (1983) and the theory of Kotarski (1989), and Lions (1971), we formulate the boundary control problem for a system governed by Neumann problem involving selfadjoint elliptic operator of 2 th order with an infinite number of variables. The inequalities which characterize the optimal control in terms of the adjoint system are obtained, it is studied in order to construct algorithms attainable to numerical computations for the approximation of the control.…”

An optimization problem for infinite order distributed parabolic systems with multiple time-varying lags

“…The parabolic operator ∂/∂t + A(t) in the state equation (1) is an infinite order parabolic operator and A(t) [24] and (Gali andEl-Saify, 1982, 1983) and [34] is given by:…”

“…The necessary and sufficient conditions of optimality for systems consists of only one equation and for (n × n) systems governed by different types of partial differential equations defined on spaces of functions of infinitely many variables and also for infinite order systems are discussed for example in [25][26][27][28]42,45] in which the argument of [46,47] were used.…”

Necessary Conditions for Control Problems Governed by Elliptic Variational Inequalities with an Infinite Number of Variables

“…Gali et al [6] presented a set of inequalities defining a control of a system governed by self-adjoint elliptic operators with an infinite number of variables.…”