Obstruction to the bilinear control of the Gross-Pitaevskii equation: an example with an unbounded potential

Chambrion, Thomas; Thomann, Laurent

doi:10.1016/j.ifacol.2019.11.796

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2023

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“…Many studies related to the control problem (1) has been developed by researchers in recent years, both in the development of its controllability and its application to some specific equations such as Schrödinger equation and Gross-Pitaevskii equation, see J. M. Ball et al [1], Nabile Boussaïd. et al [2,3], Thomas Chambrion and Laurent Thomann [4], Gunther Dirr [5], and Jonas Lampart [6].…”

Section: Introductionmentioning

confidence: 99%

On Conditions for Controllability and Local Regularity of A System of Differential Equations

Zuhri,

Soeharyadi,

Widjaja

2023

JIMS

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We consider a system of differential equations on a Banach space X given by: x'(t) = Ax(t) + u(t)f(t, x(t)), x(0) = x0, where A is an infinitesimal generator of a C0-semigroup, f : R0+ × X → X is a locally Lipschitz function, and u ∈ Lp([0, T], R) is a control defined on [0, T] with 1 < p ≤ ∞. Using the Compactness Principle and the generalization of Gronwalls Lemma, the system is shown to be controllable for a γ-bounded function f. Another result of this study is the local existence and the uniqueness of the solution of the system for locally bounded function f through weighted ω-norm.

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