Abstract and Applied Analysis
Volume 7 (2002), Issue 7, Pages 385-399
doi:10.1155/S1085337502204091
An inverse problem for a nonlinear Schrödinger
equation
Department of Mathematics, University of British Columbia, Vancouver, BC V6T 1Z2, Canada
Received 10 January 2002
Copyright © 2002 Bui An Ton. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
We study the dependence on the control q of the interval of
definition of the solution u of the Cauchy problem ιu′+Δ u=−λ|u| 2u−ιqu
in
ℝ 2×(0,T),u(x,0)=ω
in
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 ℝ 2
are established.