Stochastic Ginzburg-Landau equation on a half-line with Neumann type white-noise boundary conditions

Juárez-Campos, Beatriz; Kaikina, Elena I.; Ruiz-Paredes, Hector F.

doi:10.1016/j.jmaa.2020.123952

Cited by 2 publications

(1 citation statement)

References 19 publications

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“…In addition, the time-space fractional GL equation driven by fractional Brownian motion is concerned (Xu et al, 2019). Even stochastic nonlinear GL system on the half-line with Neumann white noise boundary conditions have been studied (Juárez-Campos et al, 2020).…”

Section: Introductionmentioning

confidence: 99%

Iterative learning control of complex Ginzburg–Landau system

Cai

Dai

Zhang

et al. 2022

Transactions of the Institute of Measurement and Control

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Different from the existing research on iterative learning control (ILC) real-valued systems, complex-valued partial differential system is studied in this paper. All variables and parameters of the system are complex, and distributed control is imposed on the system. First, the original complex system is transformed into two coupled real systems, which represent the real and imaginary parts of the original complex system, respectively. Second, a complex [Formula: see text]-type ILC algorithm is designed that the real and imaginary parts of the learning law are coupled to each other. Then, the contraction mapping principle and analytical techniques are used to ensure that the tracking error converges to zero in the sense of [Formula: see text]-norm. Finally, a numerical simulation is presented to show the effectiveness of the proposed algorithm.

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Section: Introductionmentioning

confidence: 99%

Iterative learning control of complex Ginzburg–Landau system

Cai

Dai

Zhang

et al. 2022

Transactions of the Institute of Measurement and Control

View full text Add to dashboard Cite

show abstract

Stochastic Ginzburg–Landau equation on a half-line driven by the multiplicative noise

Juárez-Campos

Kaikina

Vazquez-Esquivel

2022

Journal of Mathematical Physics

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We consider the stochastic nonlinear Ginzburg–Landau equations driven by the multiplicative noise on the half-line with Neumann brown-noise boundary conditions. We establish the existence and uniqueness of a solution to an initial-boundary value problem with values in Sobolev space H1. We are also interested in the regularity behavior of the solution, especially near the origin, where the boundary data are highly irregular.

show abstract

Stochastic Ginzburg-Landau equation on a half-line with Neumann type white-noise boundary conditions

Cited by 2 publications

References 19 publications

Iterative learning control of complex Ginzburg–Landau system

Iterative learning control of complex Ginzburg–Landau system

Stochastic Ginzburg–Landau equation on a half-line driven by the multiplicative noise

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