An inverse problem for a nonlinear Schrödinger equation

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.