## Professor Xingbin Pan(潘兴斌)

### Professor Xingbin Pan

• Professor of East China Normal University

eMail:  xbpan@math.ecnu.edu.cn

Phone Number(s):

Direct: +86-21-62233519
+86-21-54345089

Office:

Room A1501, Science Building, ZhongBei Campus
Room 335, Math Building

Research Interests:
Nonlinear partial differential equations and systems, calculus of variations, mathematical theory of superconductivity and liquid crystals.
Recent Publications (from MathSciNet):
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Selected Publications

 [56] Meissner states of 3-dimensional superconductors of type II, submitted. [55] On a linear differential operator involving Curl, submitted [54] Phase transition for potential with higher dimensional wells, submitted, (with Fanghua Lin and Changyou Wang) [53] Superconductivity near the normal state in a half-plane under the action of a perpendicular electric current and an induced magnetic field, Transactions of Amer. Math. Soc., to appear, (with Yaniv Almog and Bernard Helffer) [52] On a quasilinear system arising in the theory of superconductivity, Proc. Royal Soc. Edinburgh, vol. 141 A (2011), 397-407, (with Gary Lieberman) [51] Asymptotics of solutions of a quasilinear system involving curl, J. Math. Phys., vol. 52 (2011), article no. 023517, 34pp. [50] 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 Yaniv Almog and Bernard Helffer) [49] A Note on best Sobolev and relative iso-perimetric constants and Neumann problems in exterior domains，《中国科技论文在线》，论文编号201002-495（with Xuefeng Wang）. [48] Minimizing Curl in a multiconnected Domain, J. Math. Phys., vol. 50, no. 3, (2009), art. no. 033508. [47] On a quasilinear system involving the operator Curl, Calculus of Variations and PDE, vol. 36, no. 3 (2009), 317-342. [46] An eigenvalue variation problem of magnetic Schrodinger operator in three-dimensions, Disc. Contin. Dyn. Systems, special issue for Peter Bates’ 60th birthday, vol. 24, no. 3 (2009), 933-978. [45] A three-stage operator-splitting/ finite element method for the numerical simulation of liquid crystal flow, International Journal of Numerical Analysis and Modeling, vol. 6, no. 3 (2009), 440-454. (with R.Glowinski and P. Lin) [44] Nucleation of instability of Meissner state of superconductors and related mathematical problems, in: B. J. Bian, S. H. Li and X. J. Wang eds., Trends in Partial Differential Equations, for Prof Guangchang Dong’s 80th birthday, “Advanced Lectures in Mathematics”, ALM10, pp.323-372, Higher Education Press and International Press, Beijing-Boston, 2009. [43] Reduced Landau-de Gennes functional and surface smectic state of liquid crystals, Journal of Functional Analysis, vol. 255, no. 11 (2008), 3008-3069. (with B. Helffer) [42] Critical elastic coefficient of liquid crystals and hysteresis, Comm. Math. Phys., vol. 280, no.1, (2008), 77-121. [41] Nucleation of instability in Meissner state of 3-dimensional superconductors, Comm. Math. Phys., vol. 276, no. 3, (2007), 571-610. (with P. Bates) [40] 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. 479-517. [39] Nodal set of solutions of equations involving magnetic Schrodinger operator in three dimensions, J. Math. Phys., vol. 48, no. 5, (2007), article number 053521. [38] Magnetic field-induced instabilities in liquid crystals, SIAM J. Math. Anal., vol. 38, no. 5 (2007), 1588-1612, (with F. H. Lin) [37] Landau-de Gennes model of liquid crystals with small Ginzburg-Landau parameter, SIAM J. Math. Anal., vol.37, no.5 (2006), 1616-1648. [36] Multiple states and hysteresis for type I superconductors, J. Math. Phys.,vol.46, no.7 (2005), Article no. 073301. (with Yihong Du). [35] Surface superconductivity in 3-dimensions, Trans. Amer. Math. Soc., vol. 356 (10) (2004), 3899-3937. [34] Landau-de Gennes model of liquid crystals and critical wave number, Comm. Math. Phys., vol. 239 (1-2) (2003), 343-382. [33] Superconductivity near critical temperature, J. Math. Phys., vol. 44 (6) (2003), 2639-2678. [32] Superconducting films in perpendicular fields and effect of de Gennes parameter, SIAM J. Math. Anal., vol. 34 (4) (2003), 957-991. [31] An operator-splitting method for liquid crystal model, Comp. Phys. Comm., vol. 152 (3) (2003), 242-252, (with R. Glowinski and P. Lin) [30] Upper critical field and location of surface nucleation of superconductivity, Ann. LHP Analyse Non Lineaire, vol. 20 (1), 2003, 145-181. (with B. Helffer) [29] Surface superconductivity in applied magnetic fields above H_c2, Comm. Math. Phys., vol. 228 (2), (2002), 327-370. [28] Upper critical field for superconductors with edges and corners, Calculus of Variations and PDE, vol. 14 (4) (2002), no. 4, 447-482. [27] On a problem related to vortex nucleation of superconductivity, J. Differential Equations, vol. 182 (2002), 141-168. (with K. H. Kwek) [26] Schrodinger operators with non-degenerately vanishing magnetic fields in bounded domains, Trans. Amer. Math. Soc., vol. 354 (10) (2002), 4201-4227. (with K. H. Kwek) [25] Ginzburg-Landau system and surface nucleation of superconductivity, Methods and Applications of Analysis, vol. 8 (2) (2001), 279-300. (with K. Lu) [24] Surface nucleation of superconductivity in 3-dimension, J. Differential Equations, vol. 168 (2) (2000), 386-452. (with K. Lu) [23] Asymptotics of minimizers of variational problems involving curl functional, J. Math. Phys., vol. 41 (7) (2000), 5033-5063. (with Y. Qi) [22] Gauge invariant eigenvalue problems in R^2 and in R^2_+, Trans. Amer. Math. Soc., vol. 352 (3) (2000), 1247-1276. (with K. Lu) [21] Estimates of the upper critical field for the Ginzburg-Landau equations of superconductivity, Physica D, vol. 127 (1-2) (1999), 73-104. (with K. Lu) [20] Eigenvalue problem of Ginzburg-Landau operator in bounded domains, J. Math. Phys., vol. 40 (6) (1999), 2647-2670. (with K. Lu) [19] Yamabe problem on half spaces, Nonlinear Anal. TMA, vol. 37 (2) (1999), 161-186. (with G. Bianchi) [18] A variational problem of liquid crystals, Comm. in Applied Nonlinear Anal., vol. 5 (1) (1998), 1-31. (with Y. Yi) [17] Semilinear Neumann problem in an exterior domain, Nonlinear Anal. TMA, vol. 31 (7) (1998), 791-821. (with X. Wang) [16] Ginzburg-Landau equation with De Gennes boundary conditions, J. Differential Equations, vol. 129 (1) (1996), 136-165. (with K. Lu) [15] Least energy solutions of semilinear Neumann problems in R^4 and asymptotics, J. Math. Anal. Appl., vol. 201 (2) (1996), 532-554. (with X. Xu) [14] Singular limit of quasilinear Neumann problems, Proc. Royal Soc. Edinburgh, vol. 125A (1) (1995), 205-223. [13] Further study on the effect of boundary conditions, J. Differential Equations, vol. 117 (2) (1995), 446-468. [12] Condensation of least-energy solutions: The effect of boundary conditions, Nonlinear Anal. TMA, vol. 24 (2) (1995), 195-222. [11] Condensation of least-energy solutions of a semilinear Neumann problem, J. Partial Differential Equations, vol. 8 (1) (1995), 1-36. [10] The Melnikov method and elliptic equations with critical exponent, Indiana Univ. Math. J., vol. 43 (3) (1994), 1045-1077. (with R. Johnson and Y. Yi) [9] Singular solutions of the elliptic equation Delta u-u+u^p=0, Ann. Mat. Pura Appl., vol. 166 (4) (1994), 203-225. (with R. Johnson and Y. Yi) [8] Positive solutions of super-critical elliptic equations and asymptotics, Comm. Partial Differential Equations, vol. 18 (5-6) (1993), 977-1019. (with R. Johnson and Y. Yi) [7] Singular ground states of semilinear elliptic equations via invariant manifold theory, Nonlinear Anal. TMA, vol. 20 (11) (1993), 1279-1302. (with R. Johnson and Y. Yi) [6] On an elliptic equation related to the blow-up problem of the nonlinear Schrodinger equation, Proc. Royal Soc. Edinburgh, vol. 123A (4) (1993), 763-782. (with R. Johnson) [5] 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 (2) (1993), 323-338. [4] Blow-up behavior of ground states of semilinear elliptic equations in R^n involving critical Sobolev exponents, J. Differential Equations, vol. 99 (1) (1992), 78-107. (with X. Wang) [3] Singular behavior of least-energy solutions of a semilinear Neumann problem involving critical Sobolev exponents, Duke Math. J., vol. 67 (1) (1992), 1-20. (with W. M. Ni and I. Takagi) [2] Positive solutions of Delta u+K(x)u^p=0 without decay conditions on K(x), Proc. Amer. Math. Soc., Vol. 115 (3) (1992), 699-710. [1] Existence of singular solutions of a semilinear elliptic equation in R^n, J. Differential Equations, vol. 94 (1) (1991), 191-203.

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