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

Departmental Address:


 
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

Citations in the American Mathematical Society MathSciNet

Citations in the American Mathematical Society MathSciNet (access from outside of ECNU)

http://www.ams.org/mathscinet/mrcit/individual.html?mrauthid=236649

                 
[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201002-495with 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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