Positive and negative exact boundary controllability results for the linear Biharmonic Schr\"odinger equation
Abstract
In this paper, we study the exact boundary controllability of the linear Biharmonic Schr\"odinger equation i∂ty=-∂x4y+ γ∂x2y on a bounded domain with hinged boundary conditions and boundary control acts on the second spatial derivative at the left endpoint, where the parameter γ<0. We prove that this system is exactly controllable in time T>0, if and only if, the parameter γ 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.
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