Attractivity of Time-periodic Solutions of Ginzburg-Landau Equations of Superconductivity and Numerical Simulations

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Authors

  • Mei-Qin Zhan Department of Mathematics and Statistics, University of North Florida, Jacksonville, FL 32224, USA Author
  • Kening Wang Department of Mathematics and Statistics, University of North Florida, Jacksonville, FL 32224, USA Author

DOI:

https://doi.org/10.5890/JVTSD.2024.09.004

Abstract

It is well-known that the Ginzburg-Landau equations admit at least three time-periodic solutions. One of them describes the non-super- conductive (or normal) state and the other one describes the superconductivity state. In this paper, we investigate the uniform boundedness and attractivity of these time-periodic solutions. Moreover, numerical approximations to time-periodic solutions are also presented.

References

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[4] Konsin, P. and Sorkin, B. (2009) Time-dependent Ginzburg-Landau equations for a two-component superconductor and the doping dependence of the relaxation times of the order parameters in $YBa_2Cu_3O_{7-delta}$, Journal of Physics: Conference Series, 150.

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[7] Zhan, M. (2000), Existence of periodic solutions for Ginzburg-Landau equations of superconductivity, Journal of Mathematical Analysis and Applications, 249(2), 614-625

[8] Zhan, M. (2008), Multiplicity and stability of time-periodic solutions of Ginzburg-Landau equations of superconductivity, Journal of Mathematical Analysis and Applications, 340, 126–134

[9] Temam, R. (2000), Infinite-Dimensional Dynamical Systems in Mechanics and Physics, Springer-Verlag.

[10] Pao, C.V. (1999), Periodic solutions of parabolic systems with nonlinear boundary conditions, Journal of Mathematical Analysis and Applications, 234, 695-716

[11] Rahman, M., Wang, K., and Zhan, M. Time-periodic Solutions of Ordinary Differential Equations of Superconductivity, preprint.

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PublishedSeptember 2024

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How to Cite

Zhan, M.-Q., & Wang, K. (2026). Attractivity of Time-periodic Solutions of Ginzburg-Landau Equations of Superconductivity and Numerical Simulations. Journal of Vibration Testing and System Dynamics, 8(3), 317-328. https://doi.org/10.5890/JVTSD.2024.09.004