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Dynamics of Fractional Stochastic Ginzburg–Landau Equation Driven by Nonlinear Noise

Author

Listed:
  • Hong Lu

    (School of Mathematics and Statistics, Shandong University, Weihai 264209, China)

  • Linlin Wang

    (School of Mathematics and Statistics, Shandong University, Weihai 264209, China)

  • Mingji Zhang

    (Department of Mathematics, New Mexico Institution of Mining and Technology, Socorro, NM 87801, USA)

Abstract

In this work, we focus on the long-time behavior of the solutions of the stochastic fractional complex Ginzburg–Landau equation defined on R n with polynomial drift terms of arbitrary order. The well-posedness of the equation based on pathwise uniform estimates and uniform estimates on average are proved. Following this, the existence and uniqueness of weak pullback random attractors are establsihed.

Suggested Citation

  • Hong Lu & Linlin Wang & Mingji Zhang, 2022. "Dynamics of Fractional Stochastic Ginzburg–Landau Equation Driven by Nonlinear Noise," Mathematics, MDPI, vol. 10(23), pages 1-36, November.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:23:p:4485-:d:986285
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    References listed on IDEAS

    as
    1. Tarasov, Vasily E. & Zaslavsky, George M., 2005. "Fractional Ginzburg–Landau equation for fractal media," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 354(C), pages 249-261.
    2. Qiuying Lu & Guifeng Deng & Weipeng Zhang, 2014. "Random Attractors for Stochastic Ginzburg-Landau Equation on Unbounded Domains," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-12, June.
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    Cited by:

    1. Qi, Jianming & Li, Xinwei & Bai, Leiqiang & Sun, Yiqun, 2023. "The exact solutions of the variable-order fractional stochastic Ginzburg–Landau equation along with analysis of bifurcation and chaotic behaviors," Chaos, Solitons & Fractals, Elsevier, vol. 175(P2).

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