PAN, Xingbin

Professor

Education Background

Ph. D. (Shandong University)

Research Field
Partial differential equations, calculus of variations, mathematical theory of superconductivity, liquid crystals and electromagnetism, nonlinear Maxwell equations and Maxwell-Stokes equations
Academic Area
Mathematics and Applied Mathematics
Personal Website
https://myweb.cuhk.edu.cn/panxingbin/Home/Index
Email
panxingbin@cuhk.edu.cn
Academic Publications
  1. Ginzburg-Landau equation and Meissner states of multiply-connected superconductors, Journal of Functional Analysis, Vol. 286, No. 12 (2024), article no. 110717 (74 pages).
  2. Static and evolution equations with degenerate curls, Journal of Differential Equations, Vol. 391 (2024), 167-219.
  3. Existence of Meissner solutions to the full Ginzburg-Landau system in three dimensions, Archive for Rational Mechanics and Analysis, Vol. 248, No. 2 (2024), art. no. 17, (55 pages, with X.F. Xiang).
  4. Maxwell-Stokes system with Robin boundary condition, Calculus of Variations and Partial Differential Equations, Vol. 62, No. 6 (2023), art. no. 167.
  5. On the shape of Meissner solutions to the 2-dimensional Ginzburg-Landau system, Mathematische Annalen, Vol. 387, No. 1-2 (2023), 541-613 (with X. F. Xiang).
  6. Div-curl system with potential and Maxwell-Stokes system with natural boundary condition, Journal of Dynamics and Differential Equations, Vol. 34, No.3 (2022), 1769-1821.
  7. The general magneto-static model and Maxwell-Stokes system with topological parameters, Journal of Differential Equations, 270 (1) (2021), 1079-1137.
  8. Oscillatory patterns in the Ginzburg-Landau model driven by the Aharonov-Bohm potential, Journal of Functional Analysis, Vol. 279, No. 10 (2020), article no. 108718 (with A. Kachmar).
  9. Concentration behavior and lattice structure of surface superconductivity, Mathematical Physics, Analysis and Geometry, Vol. 22, No. 2 (2019), article no. 12 (with S. Fournais and J.-P. Miqueu).
  10. Mixed normal-superconducting states in the presence of strong electric currents, Archive for Rational Mechanics and Analysis, 223, No. 1 (2017), 419-462 (with Y. Almog and B. Helffer).
  11. Existence and regularity of solutions to quasilinear systems of Maxwell type and Maxwell-Stokes type, Calculus of Variations and Partial Differential Equations, Vol. 55, No. 6 (2016), article no.143.
  12. Partial Sobolev spaces and anisotropic smectic liquid crystals, Calculus of Variations and Partial Differential Equations, Vol. 51, No. 3 (2014), 963-998.
  13. Critical elastic coefficient of liquid crystals and hysteresis, Communications in Mathematical Physics, Vol.280, No.1 (2008), 77-121.
  14. Surface superconductivity in 3-dimensions, Transactions of the American Mathematical Society, Vol. 356, No. 10 (2004), 3899-3937.
  15. Landau-de Gennes model of liquid crystals and critical wave number, Communications in Mathematical Physics, Vol.239, No.1-2 (2003), 343-382.
  16. Surface superconductivity in applied magnetic fields above H_c2, Communications in Mathematical Physics, Vol. 228, No. 2 (2002), 327-370.