Boundary Control Problem with an Infinite Number of Variables
نویسندگان
چکیده
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. 2000 Mathematics Subject Classification. 49J20, 93C20. 1. Functions spaces. This section covers the basic notations, definitions, and properties which are necessary to present this work. Let (pk(t))k=1 be a sequence of weights, fixed in all that follows, such that 0 0, c0 is a constant [5]. The above bilinear form is coercive in W (R∞) that means π(φ,φ)≥ c‖φ‖2W (R∞), φ∈W (R∞), c constant. (2.4)
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