An inverse problem for a nonlinear Schrödinger equation. (English) Zbl 1009.35077

Summary: We study the dependence on the control \(q\) of the interval of definition of the solution \(u\) of the Cauchy problem \(\iota u'+\Delta u=-\lambda |u|{2}u-\iota qu\) in \({\mathbb{R}}^{2}\times (0,T)\), \(u(x,0)=\omega\) in \({\mathbb{R}}^{2}\), and we prove a version of Fibich’s conjecture. Feedback laws for an inverse problem of the above equation with experimental data, measured on a portion of the boundary of an open, bounded subset of \({\mathbb{R}}^{2}\) are established.


35Q55 NLS equations (nonlinear Schrödinger equations)
35B37 PDE in connection with control problems (MSC2000)
35R30 Inverse problems for PDEs
49J20 Existence theories for optimal control problems involving partial differential equations
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