An inverse problem for a nonlinear Schrödinger equation

Ton, Bui An

Abstr. Appl. Anal., Tome 7 (2002) no. 12, p. 385-399 / Harvested from Project Euclid

Résumé

We study the dependence on the control $q$ of the interval of definition of the solution $u$ of the Cauchy problem $\imath u^{\prime}+\Delta u = -\lambda|u|^{2}u -\imath q u$ 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.

Détail

Publié le : 2002-05-14
Classification:  35L05,  49J20,  49N45