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Small-time approximate controllability for the nonlinear complex Ginzburg-Landau equation with bilinear control

Published 27 Dec 2025 in math.OC and math.AP | (2512.22512v1)

Abstract: In this paper, we consider the bilinear approximate controllability for the complex Ginzburg-Landau (CGL) equation with a power-type nonlinearity of any integer degree on a torus of arbitrary space dimension. Under a saturation hypothesis on the control operator, we show the small-time global controllability of the CGL equation. The proof is obtained by developing a multiplicative version of a geometric control approach, introduced by Agrachev and Sarychev in \cite{AS05,AS06}.

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