Internal control for a non-local Schrödinger equation involving the fractional Laplace operator
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2022-02
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American Institute of Mathematical Sciences
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We analyze the interior controllability problem for a non-local Schrödinger equation involving the fractional Laplace operator (-Δ)s, s ϵ(0 1), on a bounded C1 1 domain RN. We first consider the problem in one space dimension and employ spectral techniques to prove that, for s ϵ [1/2/1), null-controllability is achieved through an L2(ωX (0,T)) function acting in a subset ω Ω of the domain. This result is then extended to the multi-dimensional case by applying the classical multiplier method, joint with a Pohozaev-type identity for the fractional Laplacian.
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Biccari, U. (2022). Internal control for a non-local Schrödinger equation involving the fractional Laplace operator. Evolution Equations and Control Theory, 11(1), 301-324. https://doi.org/10.3934/EECT.2021014