Positive and negative exact controllability results for the linear Biharmonic Schrödinger equation

Abstract

In this paper, we study the exact boundary controllability of the linear Biharmonic Schrödinger equation on a bounded domain with hinged boundary conditions and boundary control acts on the second spatial derivative at the left endpoint. We prove that this system is exactly controllable at any positive time $ T $, if and only if, the group velocity dispersion (GVD) coefficient does not belong to a critical countable set of negative real numbers. The analysis in this work is based on spectral analysis together with the nonharmonic Fourier series method.