Optimal Bilinear Control of Nonlinear Hartree Equations with Singular Potentials

Binhua Feng () and Kai Wang
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Binhua Feng: Northwest Normal University
Kai Wang: Lanzhou University

Journal of Optimization Theory and Applications, 2016, vol. 170, issue 3, No 3, 756-771

Abstract: Abstract In this paper, we consider an optimal bilinear control problem for nonlinear Hartree equations with singular potentials. We show well-posedness of the problem and existence of an optimal control. In addition, the first-order optimality system is rigorously derived. In particular, we prove Fréchet-differentiability of the objective functional. Our results improve considerably some recent results.

Keywords: Optimal bilinear control problem; Nonlinear Hartree equation; Compactness; Optimal condition; Fréchet-differentiability; 35Q55; 49J20 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10957-016-0976-0

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