Xing-Bin Pan

Publications

Xing-Bin Pan
Title:

Professor

Research

Nonlinear partial differential equations and systems, calculus of variations,
mathematical theory of superconductivity, liquid crystals and electromagnetism.

PublicationsInfo

  • [89] Regularity of a parabolic system involving curl, J. Elliptic and Parabolic Equations, 7 (2) (2021), 923-944.

         DOI 10.1007/s41808-021-00119-8. Sharedit link https://rdcu.be/czf7B. 

        arXiv:2108.00631, http://arxiv.org/abs/2108.00631.

  • [88] On a quasilinear parabolic curl system motivated by time evolution of Meissner states of superconductors, SIAM J. Math. Anal.,  53 (6) (2021), 6471-6516,  (with K.K. Kang).  

  •      https://epubs.siam.org/doi/ pdf/10.1137/20M1351643

  • [87] Long time behavior and field-induced instabilities of smectic liquid crystals, J. Functional Anal., Vol. 281, No. 3 (2021), Article no. 109036 (with Soojung Kim).

        https://www.sciencedirect.com/science/article/pii/S002212362100118X

    [86] Div-curl system with potential and Maxwell-Stokes system with natural boundary condition, J. Dynamics Differential Equations, to appear.  DOI 10.1007/s10884-021-09994-0,  Online first:  https://rdcu.be/cjMrn

  • [85] The general magneto-static model and Maxwell-Stokes system with topological parameters, J. Differential Equations, Vol. 270, No. 1 (2021), 1079-1137.

  • [84] Maxwell-Stokes system with L2 boundary data and div-curl system with potential, SN Partial Differential Equations and Applications, special issue for the 85th birthday of Prof. Dajun Guo, Vol. 1, No. 5 (2020), article no. 36, 56 pages.

  • [83] Oscillatory patterns in the Ginzburg-Landau model driven by the Aharonov-Bohm potential, J. Functional Anal., Vol. 279, No. 10 (2020), article no. 108718 (with A. Kachmar).

  • [82] Singular limits of anisotropic Ginzburg-Landau functional, J. Elliptic and Parabolic Equations, special issue for the 70th birthday of Prof. Chipot, Vol. 6No.1 (2020), 27-54.

  • [81] Variational and operator methods for Maxwell-Stokes system, Disc. Contin. Dyn. Systems, Ser. A, special issue dedicated to the 70th birthday of Prof. W.M. Ni, Vol. 40, No. 6 (2020), 3909-3955.

  • [80] Anisotropic nematic liquid crystals in an applied magnetic field, Nonlinearity, Vol. 33, No. 5 (2020), 2035-2076 (with S.J. Kim).

  • [79] Discontinuous nonlinearity and finite time extinction, SIAM J. Math. Anal., Vol. 52 No. 1 (2020), 894-926 (with J.W. Chung, Y.J. Kim and O.S. Kwon).

  • [78] Superconductivity and the Aharonov-Bohm effect, C. R. Acad. Sci. Paris, Ser. I, Vol. 357, No. 2 (2019), 216-220 (with A. Kachmar) .

  • [77] Concentration behavior and lattice structure of surface superconductivity, Mathematical Physics, Analysis and Geometry, Vol. 22, No. 2 (2019), article no. 12, 33 pp. (with S. Fournais and J.-P. Miqueu) .

  • [76] Existence and regularity of weak solutions for a thermoelectric model, Nonlinearity, Vol. 32, No. 9 (2019), 3342-3366 (with Z.B. Zhang).

  • [75] Meissner states of type II superconductors, J. Elliptic and Parabolic EquationsVol. 4, No. 2 (2018), 441-523.

  • [74] 超导与液晶边界层现象的数学问题 (Mathematical problems of boundary layer behavior of superconductivity and liquid crystals), 《中国科学:数学》481, “庆贺董光昌教授90华诞专辑 83-110页,2018.

  • [73] Existence of surface smectic states of liquid crystals, J. Functional Analysis, Vol. 274, No. 3 (2018), 900-958 (with A. Kachmar and S. Fournais).

  • [72] Quasilinear systems involving curl, Proc. Royal Soc. Edinburgh, Ser. A, Vol. 148, No. 2 (2018), 243-279 (with J. Chen)

  • [71] Directional curl spaces and applications to the Meissner states of anisotropic superconductors, J. Math. Phys., Vol. 58, No. 1 (2017), article no. 011508, 24 pages.

  • [70] 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).

  • [69] Existence and regularity of solutions to quasilinear systems of Maxwell type and Maxwell-Stokes type, Calculus of Variations and PDEs, Vol. 55, No. 6 (2016), article no.143, pp 1-43.

  • [68] A brief introduction on some mathematical problems of surface superconductivity,关于表面超导的若干数学问题. 中国科技论文在线  [2015-03-03]. http://www.paper.edu.cn/releasepaper/content/201503-2.

  • [67] Regularity of weak solutions to nonlinear Maxwell systems, J. Math. Phys., Vol. 56, No. 7 (2015), article no. 071508.

  • [66] Partial Sobolev spaces and anisotropic smectic liquid crystals, Calc. Var. PDE, Vol. 51, No. 3 (2014), 963-998.

  • [65] An extended magnetostatic Born-Infeld model with a concave lower order term, J. Math. Phys., Vol. 54, No. 11 (2013), article no. 111501 (with J. Chen).

  • [64] Functionals with operator curl in an extended magnetostatic Born-Infeld model,  SIAM J. Math. Anal., Vol. 45, No. 4 (2013), 2253-2284 (with J. Chen)

  • [63] Superconductivity near the normal state in a half-plane under the action of a perpendicular electric current and an induced magnetic field, Trans. Amer. Math. Soc., Vol. 365, No. 3 (2013), 1183-1217 (with Y. Almog and B. Helffer).

  • [62] Superconductivity near the normal state in a half-plane under the action of a perpendicular electric current and an induced magnetic field II : the large conductivity limit, SIAM J. Math. Anal., Vol. 44, No. 6 (2012), 3671-3733 (with Y. Almog and B. Helffer).

  • [61] Phase transition for potentials of high-dimensional wells, Comm. Pure Appl. Math., Vol. 65, No. 6 (2012)833-888 (with F.H. Lin and C.Y. Wang).

  • [60] On a quasilinear system arising in theory of superconductivity, Proc. Royal Soc. Edinburgh, Ser. A. vol. 141, No. 2 (2011), 397-407 (with G. Lieberman)

  • [59] Asymptotics of solutions of a quasilinear system involving curl, J. Math. Phys., Vol.52, No. 2 (2011), article no. 023517, 34pp.

  • [58] Superconductivity near the normal state under the action of electric currents and induced magnetic fields in R^2, Comm. Math. Phys., Vol.300, No. 1 (2010), 147-184 (with Y. Almog and B. Helffer).

  • [57] Nucleation of instability of Meissner state of superconductors and related mathematical problems, in: Trends in Partial Differential Equations, for Prof Guangchang Dong’s 80th birthday,  pp.323-372, Higher Education Press and International Press, Beijing-Boston, 2009.

  • [56] On a quasilinear system involving the operator curl, Calc. Var. PDE, Vol. 36, No. 3 (2009), 317-342.

  • [55] On some spectral problems and asymptotic limits occurring in the analysis of liquid crystals, Cubo Mathematical Journal, Vol. 11, No. 5 (2009), 1-22 (with B. Helffer).

  • [54] An eigenvalue variation problem of magnetic Schrodinger operator in three-dimensions, Disc. Contin. Dyn. Systems, Ser. A, special issue dedicated to the 70th birthday of Prof. P. Bates, Vol. 24, No.3 (2009), 933-978.

  • [53] A three-stage operator-splitting/ finite element method for the numerical simulation of liquid crystal flow, International Journal of Numerical Analysis & Modeling, Vol. 6, No. 3 (2009), 440-454 (with R. Glowinski and P. Lin).

  • [52] Minimizing curl in a multiconnected domain, J. Math. Phys., Vol.50, No.3 (2009), article no. 033508.

  • [51] Critical fields and nucleation of superconductors and liquid crystals, Proceedings of Fourth International Congress of Chinese Mathematicians: Invited Lecturesvol. 3, 778-792, International Press, 2007.

  • [50] Reduced Landau-de Gennes functional and surface smectic state of liquid crystals, J. Functional Analysis, Vol. 255, No.11 (2008), 3008-3069 (with B. Helffer).

  • [49] Critical fields of liquid crystals, inProceedings of Moving Interface Problems and Applications in Fluid Dynamics, B. C. Khoo, Z. L. Li and P. Lin eds., Contemporary Mathematics, Vol. 466 (2008), Amer. Math. Soc., 121-134.

  • [48] Critical elastic coefficient of liquid crystals and hysteresis, Comm. Math. Phys., Vol.280, No.1 (2008), 77-121.

  • [47] Nucleation of instability in Meissner state of 3-dimensional superconductors, Comm. Math. Phys., Vol. 276, No. 3 (2007), 571-610 (with P. Bates).

  • [46] Analogies between superconductors and liquid crystals: nucleation and critical fields, in: Asymptotic Analysis and Singularities, Advanced Studies in Pure Mathematics, Mathematical Society of Japan, Tokyo, Vol.47-2 (2007); pp. 479-518.

  • [45] Nodal set of solutions of equations involving magnetic Schrodinger operator in three dimensions, J. Math. Phys., Vol. 48, No. 5 (2007), article no. 053521.

  • [44] Magnetic field-induced instabilities in liquid crystals, SIAM J. Math. Anal., Vol. 38, No. 5 (2006/2007), 1588-1612 (with F. H. Lin).

  • [43] Nucleation of superconductivity and smectics, Electronic Proceedings of Fourth Asia Mathematical Conference, 20-23 July 2005, National University of Singapore. 15 pages.

  • [42] Landau-de Gennes model of liquid crystals with small Ginzburg-Landau parameter, SIAM J. Math. Anal., Vol.37, No.5 (2006), 1616-1648.

  • [41] Multiple states and hysteresis for type I superconductors, J. Math. Phys., Vol. 46, No.7 (2005), Article no. 073301, 34 pp. (with Y.H. Du).

  • [40] Surface superconductivity in 3-dimensions, Trans. Amer. Math. Soc., Vol. 356, No. 10 (2004), 3899-3937.

  • [39] Landau-de Gennes model of liquid crystals and critical wave number, Comm. Math. Phys.Vol.239, No.1-2 (2003), 343-382.

  • [38] Superconducting films in perpendicular fields and the effect of the de Gennes parameter, SIAM J. on Mathematical Analysis, vol. 34, No. 4 (2003), 957-991.

  • [37] An operator-splitting method for liquid crystal model, Comp. Phys. Comm., Vol. 152, No.3 (2003), 242-252 (with R. Glowinski and P. Lin).

  • [36] Superconductivity near critical temperature, J. Math. Phys., Vol. 44, No.6 (2003), 2639-2678.

  • [35] Ginzburg-Landau system and superconductivity near critical temperature, in: Recent Advances in Computational Science and Engineering, H. P. Lee and K. Kumar eds., Imperial College Press, 2002, pp 722-725.

  • [34] Upper critical field and location of surface nucleation of superconductivity, Ann. IHP Analyse Non Lineaire, Vol. 20, No.1 (2003), 145-181(with B. Helffer).

  • [33] Surface superconductivity in applied magnetic fields above H_c2, Comm. Math. Phys., Vol. 228, No. 2 (2002), 327-370.

  • [32] Upper critical field for superconductors with edges and corners, Calculus of Variations and PDE, Vol. 14, No. 4 (2002), 447-482.

  • [31] On a problem related to vortex nucleation of superconductivity, J. Differential Equations, Vol. 182, No. 1 (2002), 141-168 (with K. H. Kwek).

  • [30] Schrodinger operators with non-degenerately vanishing magnetic fields in bounded domains, Trans. Amer. Math. Soc., Vol. 354, No. 10 (2002), 4201-4227 (with K. H. Kwek) .

  • [29] Ginzburg-Landau system and surface nucleation of superconductivity, Methods and Applications of Analysis, Vol. 8, No. 2 (2001), 279-300 (with K.N. Lu) .

  • [29] Surface nucleation of superconductivity in 3-dimension, J. Differential Equations, Vol. 168, No. 2 (2000), 386-452 (with K.N. Lu). 

  • [27] Asymptotics of minimizers of variational problems involving curl functional, J. Math. Phys., Vol. 41, No. 7 (2000), 5033-5063 (with Y.W. Qi).

  • [26] Gauge invariant eigenvalue problems in R^2 and in R^2_+, Trans. Amer. Math. Soc., Vol. 352, No. 3 (2000), 1247-1276 (with K.N. Lu).

  • [25] Estimates of the upper critical field for the Ginzburg-Landau equations of superconductivity, Physica D, Vol. 127, No. 1-2 (1999), 73-104 (with K.N. Lu).

  • [24] Eigenvalue problem of Ginzburg-Landau operator in bounded domains, J. Math. Phys., Vol. 40, No. 6 (1999), 2647-2670 (with K.N. Lu).

  • [23] Yamabe equations on half spaces, Nonlinear Anal. TMA, Vol. 37, No. 2 (1999), 161-186 (with G. Bianchi).

  • [22] A variational problem of liquid crystals, Comm. in Applied Nonlinear Anal., Vol. 5, No. 1 (1998), 1-31 (with Y.F. Yi).

  • [21] Semilinear Neumann problem in exterior domains, Nonlinear Anal. TMA, Vol. 31, No. 7 (1998), 791-821 (with X.F. Wang).

  • [20] The first eigenvalue of Ginzburg-Landau operator, in: Differential Equations and Applications, P. Bates et al. eds., International Press (1997), 215-226 (with K.N. Lu).

  • [19] Ginzburg-Landau equation with De Gennes boundary condition, J. Differential Equations, Vol. 129, No. 1 (1996), 136-165 (with K.N. Lu).

  • [18] Least energy solutions of semilinear Neumann problems in R^4 and asymptotics, J. Math. Ana. Appl., Vol. 201, No. 2 (1996), 532-554 (with X.W. Xu).

  • [17] Singular limit of quasilinear Neumann problems, Proc. Royal Soc. Edinburgh, Ser. A, Vol. 125, No. 1 (1995), 205-223.

  • [16] Further study on the effect of boundary conditions, J. Differential Equations, Vol. 117, No. 2 (1995), 446-468.

  • [15] Condensation of least-energy solutions: The effect of boundary conditions, Nonlinear Anal. TMA, Vol. 24, No. 2 (1995), 195-222.

  • [14] Condensation of least-energy solutions of a semilinear Neumann problem, J. Partial Differential Equations, Vol. 8, No. 1 (1995), 1-35.

  • [13] Semilinear Neumann problems and related topics, in: Nonlinear Analysis and Applications, Dajun Guo ed., Bejing Science and Technology Press (1994), Bejing, 37-48.

  • [12] The Melnikov method and elliptic equations with critical exponent, Indiana Univ. Math. J., Vol. 43, No. 3 (1994), 1045-1077 (with R. Johnson and Y.F. Yi).

  • [11] Singular solutions of the elliptic equation Delta u-u+u^p=0, Annali di Matematica Pura ed Applicata, Vol. 166, No. 4 (1994), 203-225 (with R. Johnson and Y.F. Yi).

  • [10] Positive solutions of super-critical elliptic equations and asymptotics, Comm. Partial Differential Equations, Vol. 18. No. 5-6 (1993), 977-1019 (with R. Johnson and Y.F. Yi).

  • [9] Singular ground states of semilinear elliptic equations via invariant manifold theory, Nonlinear Anal. TMA, Vol. 20, No. 11 (1993), 1279-1302 (with R. Johnson and Y.F. Yi).

  • [8] On an elliptic equation related to the blow-up phenomenon in the nonlinear Schrodinger equation, Proc. Royal Soc. Edinburgh, Ser. A, Vol. 123, No. 4 (1993), 763-782 (with R. Johnson).

  • [7] Positive solutions of the elliptic equation Delta u+u^{(n+2)/(n-2)}+K(x)u^q=0 in R^n and in balls, J. Math. Anal. Appl., Vol. 172, No. 2 (1993), 323-338.

  • [6] Blow-up behavior of ground states of semilinear elliptic equations in R^n involving critical Sobolev exponents, J. Differential Equations, Vol. 99, No. 1 (1992), 78-107 (with X.F. Wang).

  • [5] Singular behavior of least-energy solutions of a semilinear Neumann problem involving critical Sobolev exponents, Duke Math. J., Vol. 67, No. 1 (1992), 1-20 (with W. M. Ni and I. Takagi).

  • [4] Positive solutions of Delta u+K(x)u^p=0 without decay conditions on K(x), Proc. Amer. Math. Soc., Vol. 115, No. 3 (1992), 699-710.

  • [3] Existence of singular solutions of a semilinear elliptic equation in R^n, J. Differential Equations, Vol. 94, No. 1 (1991), 191-203.

  • [2] Solutions of elliptic equation Delta u+K(x)e^{2u}=f(x),  J. Partial Differential Equations, Vol. 4, No. 2 (1991), 36-44.

  • [1] Operator sequences and measure of noncompactness, Chinese Ann. Math., Ser. A, Vol. 11, No. 2 (1990), 147-153.