El-Saify, Hussain A. Boundary control problem with an infinite number of variables. (English) Zbl 0999.49003 Int. J. Math. Math. Sci. 28, No. 1, 57-62 (2001). Summary: Using a previous result by I. M. Gali and H. A. El-Saify [J. Optimization Theory Appl. 39, 293-298 (1983; Zbl 0502.49013)] and the theory of W. Kotarski [J. Optimization Theory Appl. 60, No. 1, 33-41 (1989; Zbl 0632.49013)], and 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. Cited in 6 Documents MSC: 49J20 Existence theories for optimal control problems involving partial differential equations 93C20 Control/observation systems governed by partial differential equations Keywords:boundary control; Neumann problem; selfadjoint elliptic operator; optimal control Citations:Zbl 0502.49013; Zbl 0632.49013; Zbl 0203.09001 PDFBibTeX XMLCite \textit{H. A. El-Saify}, Int. J. Math. Math. Sci. 28, No. 1, 57--62 (2001; Zbl 0999.49003) Full Text: DOI EuDML