Boundary control problem with an infinite number of variables (Q1599615)

Summary: Using a previous result by \textit{I. M. Gali} and \textit{H. A. El-Saify} [J. Optimization Theory Appl. 39, 293-298 (1983; Zbl 0502.49013)] and the theory of \textit{W. Kotarski} [J. Optimization Theory Appl. 60, No. 1, 33-41 (1989; Zbl 0632.49013)], and \textit{J.-L. Lions} [``Optimal control of systems governed by partial differential equations'' (1971; Zbl 0203.09001)], we formulate the boundary control problem for a system governed by the Neumann problem involving a selfadjoint elliptic operator of \(2\ell\)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.