Panxingbin

Research interests:

Partial differential equations‚ calculus of variation‚ mathematical theory of liquid crystals and superconductivity.

Citations in the American Mathematical Society MathSciNet: 

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

 

 

[55] Superconductivity near the normal state in a half-plane under the action of a
perpendicular electric current and an induced magnetic field, part II : the large conductivity limit, SIAM J. Math. Anal., 44(6) (2012), 3671-3733. (with Yaniv Almog and Bernard Helffer)

 

[55] Phase transition for potential with higher dimensional wells‚ Communications on Pure and Applied Mathematics‚ 65(6)(2012)‚883-888‚ (with Fanghua Lin and Changyou Wang)

 

[54] Superconductivity near the normal state in a half-plane under the action of a perpendicular electric current and an induced magnetic field‚ Transactions of AMS‚ 365(3)(2013), 1183-1217. (with Yaniv Almog and Bernard Helffer)

 

[53] On a quasilinear system arising in the theory of superconductivity‚ Proc. Royal Soc. Edinburgh‚ vol. 141 A (2011)‚ 397-407. (with Gary Lieberman)

[52]  Asymptotics of solutions of a quasilinear system involving curl‚ J. Math. Phys.‚ vol. 52 (2011)‚ article no. 023517‚ 34pp.

 

[51]  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)

[50]  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‚发表日期2010年2月17日.（with Xuefeng Wang）.

[49] 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‚ "Advanced Lectures in Mathematics"‚ ALM10‚ pp.323-372‚ Higher Education Press and International Press‚ Beijing-Boston‚ 2009.

[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 Curl operator‚ Calculus of Variation and PDE‚ vol. 36‚ no. 3‚(2009)‚ 317-342.

[46] 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).

[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] An eigenvalue variation problem of magnetic Schrodinger operator in three-dimensions‚ Disc. Contin. Dyn. Systems‚ Ser. A‚ special issue for Peter Bates´ 60th birthday‚ vol. 24‚ no. 3‚ (2009)‚ 933-978.

[43] 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)

[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. Ana. 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.

 

 

 

 

 

 

2013 Spring semester

1. Complex Analysis

复变函数

(基地班1，周二下午1:00-2:40，周四下午1:00-2:40， 3#310）

2. Reading course for graduate students on nonlinear PDEs and systems (10)

“非线性偏微分方程与方程组论文”论文选读

（周二下午3:00-4:30，周四下午3:00-4:30，4#207）

 

2012 Fall semester

1. Homogenization 论文选读，周二下午1:00-4:00‚ 4#208）

2. Reading course for graduate students on nonlinear PDEs and systems (9), 周四下午1:00-4:00‚ 4#207）

 

 

 

2012 Spring semester

1. Complex Analysis

复变函数

(基地班‚周二下午1:00-2:40‚3#219；周四下午1:00-2:40‚ 3#327）

2. Reading course for graduate students on nonlinear PDEs and systems (8)

“非线性偏微分方程与方程组论文”论文选读

（周二下午3:00-4:30‚周四下午3:00-4:30‚4#208）

 

2011 Spring semester

1. Partial differential equations in mathematical physics

数理方程

(基地班‚周二上午10:00-11:50‚单周周五上午10:00-11:50‚ 3#310）

2. Reading course for graduate students on nonlinear PDEs and systems (7)

“非线性偏微分方程与方程组论文”论文选读

（周二下午1:00-3:30‚4#208）

3.New Graduate Course: The Mathematics of Diffusion and Curl

（lecturers: Prof Wei-Ming Ni (part 1)‚ me (part 2)

  《扩散与旋度的数学理论》

 

 

(每周二、四下午1:00-3:30‚ 闵行校区数学楼102报告厅。第一次上课日期：3月8日)

 

2010 Fall semester

1. Regularity theory of elliptic PDEs of second order

二阶椭圆型偏微分方程正则性理论

（周二下午1:00-3:30‚4#208）

2. Reading course for graduate students on nonlinear PDEs and systems (6)

“非线性偏微分方程与方程组论文”论文选读

（周四下午1:00-3:30‚4#222）

 

 

 

2010 Spring semester

1. Partial differential equations in mathematical physics

2. Reading course for graduate students on nonlinear PDEs and systems (5)

 

2009 Spring semester

1. Regularity theory of elliptic PDEs of second order

2. Partial differential equations in mathematical physics

3. Reading course for graduate students on nonlinear PDEs and systems (4)

 

2008 Fall semester

1. Quasilinear parabolic partial differential equations

2. Reading course for graduate students on nonlinear PDEs and systems (3)

 

2008 Spring semester

1. Parabolic partial differential equations

2. Partial differential equations in mathematical physics

3. Reading course for graduate students on nonlinear PDEs and systems (2)

 

2007 Fall semester

1. Real Analysis for graduate students

2. Quasilinear elliptic partial differential equations and systems

3. Reading course for graduate students on nonlinear PDEs and systems (1)

 

2007 Spring semester

1. Regularity theory of elliptic PDEs of second order

2. Partial differential equations in mathematical physics

 

2006 Fall semester

1. Real Analysis for graduate students

2. Geometric measure theory

 

2006 Spring semester

1. Partial differential equations in mathematical physics

2. Selected topics in partial differential equations

3. Harmonic analysis (2)

 

2005 Fall semester

1. Real Analysis for graduate students

2. Regularity theory of elliptic PDEs of second order

3. Harmonic analysis (1)

 

2004 Fall semester

1. Regularity theory of elliptic PDEs of second order

2. Nonlinear PDEs