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基本情况

姓  名:

郑神州

职  务:

博士生导师

职  称:

教授

学  历:

研究生

学  位:

博士

通信地址:

北京交通大学理学院

邮  编:

100044

办公电话:

010-51682054-118

电子邮箱:

shzhzheng@bjtu.edu.cn

教育背景

教育经历:

    • 1994/09-1997/07  复旦大学数学研究所, 博士研究生;
    • 1991/09-1994/07  北京师范大学数学系, 硕士研究生;

    研究工作经历:

    •  2017/05-2017/07  西班牙巴斯克应用数学中心合作研究项目;   
    •  2013/07-2013/08  南开大学陈省身数学研究所, 访问教授;
    •  2011/09-012/09   美国肯塔基大学,芝加哥大学,普渡大学,德克萨斯大学-Arlington分校访问学者;
    •  2008/02-2008/05  美国University of Texas-Pan American,访问教授;
    •  2007/09-2007/10  南开大学陈省身数学研究所,访问教授;
    •  2005/10-现在    北京交通大学理学院 教授
    •  2002/08-2002/12  中国科学院 系统科学研究所,访问学者;
    •  2001/02-2001/06  中国科学院应用数学研究所,访问学者;
    •  2000/07-2005/10  北京交通大学理学院 副教授;
    •  1997/07-2000/10  北京交通大学理学院 讲师 

工作经历

研究兴趣: 偏微分方程理论及应用;共形和拟共形几何理论及应用; 复分析与特殊函数论; Hardy测不准原理。

研究方向

  • 非线性系统理论与应用
  • 微分方程理论与应用

招生专业

  • 系统理论硕士
  • 应用数学硕士
  • 应用数学博士

科研项目

  1. 国家自然科学基金“国际合作项目”:调和分析与微分方程, 2016-09-010--2018-01-31, 主持
  2. 铁路总公司(原铁道部),动车组运用维护技术研究——动车组高级修错峰维修计划研究, 2015-06-01--2016-12-31, 参加
  3. 中车集团:高速列车车体结构动力模型研究与应用, 2015-08-01--2016-10-31, 主持
  4. 国家自然科学基金“面上”:抛物和椭圆型方程和方程组的若干问题,2014-01-01--2017-12-31, 主持
  5. 国家自然科学基金“面上”:具间断系数非线性退化椭圆问题的正则性研究,2011-01-01--2013-12-31,主持
  6. 北京交通大学:北京市轨道交通设施养护质量考评量化指标体系研究,2010-07-20--2010-12-31, 参加
  7. 北京交通大学:城市轨道交通系统测试分析,2009-12-21--2010-03-31,参加
  8. 北京交通大学:井间三分量地震波场反演,2007-07-01--2009-06-30,参加
  9. 国家自然科学基金“面上”:与平均曲率有关的非线性椭圆方程,2007-01-01--2009-12-31,参加
  10. 校科技基金:边值问题在弹性界面衔接和裂纹问题上的应用,2004-12-01--2006-12-01,主持
  11. 校科技基金:形变的数学理论及在工程力学中的应用,2002-11-01--2004-11-12,主持
  12. 教育部:面向MIS的预测分析构件的研究与开发,2002-01-01--2003-01-01,参加

教学工作

讲授本科课程:高等数学、线性代数、几何代数、空间解析几何、复变函数与积分变换、数理方程(复旦版)、偏微分方程(周蜀林主编)、概率论和数理统计、计算方法、运筹学等几乎所有本科课程.

研究生课程:偏微分方程现代理论、Sobolev空间、椭圆偏微分方程、抛物性偏微分方程、数学物理、数值分析、数理统计、场论、特殊函数等课程.

辅导北京市高等数学竞赛,大学生数学建模竞赛,发表教学论文.

论文/期刊

    在国际知名刊物: Transactions of Amer. Math. Soc., Journal of Functional Analysis, Journal of Differential Equations, Proceedings of Amer. Math. Soc., Discrete Conti. Dyn. Syst. A/B, Nonlinear Analysis A/B, Mathematische Nachrichten, Complex Variables and Elliptic Equations, Results in Mathematics, Dynamics of  Part. Diff. Equ., Elect. Journal Differential Equations, IMA J. Applied Math., Z. angew. Math. Phys., J. Math. Anal. Appl., Diff. and Integral Equ., Boundary Value Problems, Comm. Pure  Appl. Anal., Mediteranean J. Math.等发表了100余篇论文,其中SCI为60篇,这些成果被国内外同行广泛参考和引用。部分被美国数学会Mathematical Review论文有:


  1. Lorentz estimates for asymptotically regular fully nonlinear parabolic equations, Accepted by Math. Nachrichten,2017 (with J. Zhang).

  2. Lorentz estimates for the gradient of weak solutions to elliptic obstacle problems with partially BMO coefficients,Boundary Value Problems, 2017,DOI 10.1186/s13661-017-0859-9(with H.Tian).

  3. Monotonicity and convexity of the ratios of the first kind modified Bessel functions and applications, accepted by Math. Inequal. Appl., 2017(with Z. Yang).

  4. Global weighted Lorentz estimates to nonlinear parabolic equations over nonsmooth domains, J. Math. Anal. Appl. 456 (2017) 1238–1260 (H.Tian).

  5. Weghted Lorentz and Lorentz-Morrey estimates to viscosity solutions offully nonlinear elliptic equations, COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 2017,https://doi.org/10.1080/17476933.2017.1357707 (with J. Zhang).

  6. Orlicz estimates for nondivergence linear elliptic equations with partially BMO coefficients, COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 2017, https:// doi.org/10.1080/17476933.2017.1357707 (with H. Li and J. Zhang).

  7. Sharp bounds for the ratio of modified Bessel functions, Mediterr. J. Math. (2017) 14:169,DOI 10.1007/s00009-017-0971-1 (with Z. Yang)

  8. Partial regularity in Morrey spaces for quasi-linear subelliptic systems, Chinese Ann. Math. Ser. A,Vol.38,No.1,2017//Chinese Journal of Contemporary Mathematics, 2017, Vol. 38, No. 1, pp. 1-14(with H. Yu and Z. Zhang)

  9. New sharp approximations involving incomplete gamma functions, Results in Math., 2017, Online First(with T. Lou, H. Lv, Z.Yang).

  10. Lorentz estimates for asymptotically regular fully nonlinear elliptic equations,  Electron. J. Differential Equations, Vol. 2017 (2017), No. 120, pp. 1-13(Y.Wang and J.Zhang).

  11. Sharp inequalities for tangent function with applications. J. Inequal. Appl. 2017, Paper No. 94, 17 pp(with H. Lv, Z.Yang,T. Lou)

  12. The monotonicity and convexity for the ratios of modified Bessel functions of the second kind and applications. Proc. Amer. Math. Soc. 145  (2017), no. 7, 2943–2958(with Z. Yang).

  13. Uniformly nondegenerate elliptic equations with partially BMO coefficients in nonsmooth domains. Nonlinear Anal. 156 (2017), 90–110(with H.Tian).

  14. Weighted Lorentz estimates for nondivergence linear elliptic equations with partially BMO coefficients. Commun. Pure Appl. Anal.16  (2017)  no. 3, 899–914(with J. Zhang).

  15. Lorentz estimates for fully nonlinear parabolic and elliptic Equations. Nonlinear Analysis 148 (2017) 106–125(with J. Zhang).

  16. Hölder continuity to subelliptic A-harmonic equations under the natural growth.(Chinese) Acta Math. Appl. Sin. 39 (2016), no. 5, 689–700(with H. Yu and J. Wang).

  17. Yang, Zhen-Hang; Zheng, Shen-Zhou Monotonicity of a mean related to polygamma functions with an application. J. Inequal. Appl.  2016 2016:216, 10 pp.

  18. Sun, Bang-Cheng; Liu, Zhi-Ming; Li, Qiang; Zheng, Shen-Zhou Lp-estimates for quasilinear subelliptic equations with VMO coefficients under the controllable growth. Bound. Value Probl. 2016,2016:148, 18 pp.

  19. Zhang, Junjie; Zheng, Shenzhou Lorentz estimates for asymptotically regular elliptic equations in quasiconvex domains. Electron. J. Differential Equations 2016, Paper No. 142, 13 pp.

  20. Sun, Bang-Cheng; Liu, Zhi-Ming; Li, Qiang; Zheng, Shen-Zhou The monotonicity and convexity of a function involving psi function with applications. J. Inequal. Appl. 2016, 2016:151, 17 pp.

  21. Zheng, Shenzhou A compactness result for polyharmonic maps in the critical dimension. Czechoslovak Math. J. 66(141) (2016), no. 1,137–150.

  22. Cheng, Cui-Ping; Li, Wan-Tong; Wang, Zhi-Cheng;Zheng, Shenzhou Traveling waves connecting equilibrium and periodic orbit for a delayed population model on a two-dimensional spatial lattice. Internat. J. Bifur. Chaos Appl. Sci. Engrg. 26 (2016), no. 3, 1650049, 13 pp.

  23. Yu, Haiyan; Zheng, Shenzhou Morrey estimates for subelliptic p-Laplace type systems with VMO coefficients in Carnot groups.Electron. J. Differential Equations 2016, Paper No. 33, 14 pp.

  24. Zhang, Junjie; Zheng, Shenzhou Lorentz estimate for nonlinear parabolic obstacle problems with asymptotically regular nonlinearities. Nonlinear Anal. 134 (2016), 189–203.

  25. Yu, Haiyan; Zheng, Shenzhou; Tong, Yuxia An alternative approach to partial regularity of quasilinear elliptic systems with VMO coefficients. J. Inequal. Appl. 2016, 2016:20, 13 pp.

  26. Tong, Yu Xia; Zheng, Shen Zhou; Yu, Hai Yan Local Hölder continuity of the gradients of weak solutions to A-harmonic equation with variable exponents. (Chinese) Acta Math. Sci. Ser. A Chin. Ed. 35 (2015),no. 4, 656–667.

  27. Yu, Haiyan; Zheng, Shenzhou BMO estimate to A-harmonic systems with discontinuous coefficients. Nonlinear Anal. Real World Appl. 26 (2015), 64–74.

  28. Zheng, Shen Zhou A local Hölder estimate of (K1,K2)-quasiconformal mappings between hypersurfaces. Acta Math. Sin. (Engl. Ser.)31 (2015), no. 9, 1379–1390.

  29. Zhang, Jinjie; Zheng, Shenzhou On refined Hardy-Knopp type inequalities in Orlicz spaces and some related results. J. Inequal. Appl.2015, 2015:169, 17 pp.

  30. Zheng, Shenzhou A strong convergence of the weak gradient to A-harmonic type operators with L1 data. J. Math. Anal. Appl. 430(2015), no. 1, 381–389.

  31. Yu, Haiyan; Zheng, Shenzhou Optimal partial regularity for quasilinear elliptic systems with VMO coefficients based on A-harmonic approximations. Electron. J. Differential Equations 2015, No. 16, 12 pp.

  32. Zheng, Shenzhou; Feng, Zhaosheng Regularity of subelliptic p  -harmonic systems with subcritical growth in Carnot group. J. Differential Equations 258 (2015), no. 7, 2471–2494. 

  33. Wang, Jie; Yu, Hai Yan; Zheng, Shen Zhou Interior Hölder estimate to semilinear subelliptic equations under the natural growth. (Chinese) Acta Math. Sci. Ser. A Chin. Ed. 34 (2014), no. 6, 1397–1407.

  34. Tong, Yuxia; Zheng, Shenzhou; Gu, Jiantao Higher integrability for very weak solutions of inhomogeneous A  -harmonic form equations. J. Appl. Math. 2014, Art. ID 308751, 9 pp. 

  35. Tong, Yuxia; Gu, Jiantao; Zheng, Shenzhou Zeros for the gradients of weakly A -harmonic tensors. J. Appl. Math. 2014, Art. ID 231248, 5 pp. 

  36. Rao, Jie Sheng; Zheng, Shen Zhou Self-improving regularity of weakly quasiregular mappings in Heisenberg groups. (Chinese) Chinese Ann. Math. Ser. A 34 (2013), no. 5, 579–588. 

  37. Zheng, Shenzhou Energy quantization for approximate H-surfaces and applications. Electron. J. Differential Equations 2013, No. 177, 13 pp. 

  38. Wang, Changyou; Zheng, Shenzhou Energy identity for a class of approximate biharmonic maps into sphere in dimension four. Discrete Contin. Dyn. Syst. 33 (2013), no. 2, 861–878.

  39. Zheng, Shen Zhou Regularity of a class of degenerate elliptic equations with discontinuous coefficients under controllable growth. (Chinese) J. Systems Sci. Math. Sci. 32 (2012), no. 5, 549–561.

  40. Zheng, Shen Zhou; Lu, Han Fang Liouville theorems on subelliptic quasilinear equations in unbounded exterior domain. (Chinese) Acta Math. Sci. Ser. A Chin. Ed. 32 (2012), no. 4, 644–653. 

  41. Zheng, Shenzhou Weak compactness of biharmonic maps. Electron. J. Differential Equations 2012, No. 190, 7 pp. 

  42. Feng, Zhaosheng; Tian, Jing; Zheng, Shenzhou; Lu, Hanfang Travelling wave solutions of the Burgers-Huxley equation. IMA J. Appl. Math. 77 (2012), no. 3, 316–325. 

  43. Wang, Changyou; Zheng, Shenzhou Energy identity of approximate biharmonic maps to Riemannian manifolds and its application. J. Funct. Anal. 263 (2012), no. 4, 960–987. 

  44. Zheng, Shenzhou; Feng, Zhaosheng Green functions for a class of nonlinear degenerate operators with X-ellipticity. Trans. Amer. Math. Soc. 364 (2012), no. 7, 3627–3655.

  45. Gao, Hong-Ya; Zheng, Shen-Zhou; Yue, Ying-Qiang Beltrami system with two characteristic matrices and variable coefficients. Boundary value problems, integral equations and related problems, 170–178, World Sci. Publ., Hackensack, NJ, 2011. 

  46. Zheng, Shenzhou; Zheng, Xueliang; Feng, Zhaosheng Optimal regularity for A -harmonic type equations under the natural growth. Discrete Contin. Dyn. Syst. Ser. B 16 (2011), no. 2, 669–685.

  47. Wang, Chun Hua; Zheng, Shen Zhou Lp,λ -regularity for a class of degenerate elliptic equations with discontinuous coefficients. (Chinese) J. Systems Sci. Math. Sci. 30 (2010), no. 2, 157–172. 35J60 

  48. Zheng, Shen Zhou; Lu, Han Fang An application of the Green function to the interior Hölder continuity of weak solutions to X -elliptic equations. (Chinese) Chinese Ann. Math. Ser. A 31 (2010), no. 3, 295–304. 

  49. Zheng, Shen Zhou; Wang, Xi Fen Regularity of very weak solutions for a class of quasilinear subelliptic equations. (Chinese) Acta Math. Sci. Ser. A Chin. Ed. 30 (2010), no. 2, 432–439.

  50. Lu, Han Fang; Zheng, Shen Zhou The Green function method for the Hölder continuity of elliptic equations in divergence form. (Chinese) Acta Math. Sci. Ser. A Chin. Ed. 29 (2009), no. 5, 1160–1166. 

  51. Feng, Zhaosheng; Zheng, Shenzhou; Gao, David Y. Traveling wave solutions to a reaction-diffusion equation. Z. Angew. Math. Phys. 60 (2009), no. 4, 756–773. 

  52. Wang, Yuandi; Zheng, Shengzhou The existence and behavior of solutions for nonlocal boundary problems. Bound. Value Probl. 2009, Art. ID 484879, 17 pp. 

  53. Feng, Zhaosheng; Zheng, Shenzhou; Lu, Hanfang Green's function of non-linear degenerate elliptic operators and its application to regularity. Differential Integral Equations 21 (2008), no. 7-8, 717–741. 

  54. Zheng, Shen Zhou; Zhang, La Ping Everywhere interior regularity for p -harmonic form systems with the subcritical growth. (Chinese) Acta Math. Sinica (Chin. Ser.) 51 (2008), no. 5, 1001–1014. 

  55. Zheng, Shen Zhou Regularity for quasi-linear degenerate elliptic equations with VMO coefficients. Acta Math. Sin. (Engl. Ser.) 24 (2008), no. 11, 1909–1924. 

  56. Zheng, Xue Liang; Zheng, Shen Zhou Sharp Hölder exponents for nonlinear degenerate elliptic equations with natural growth. (Chinese) Acta Math. Sinica (Chin. Ser.) 51 (2008), no. 4, 735–748.

  57. Zheng, Shen Zhou; Zhao, Shu Le Full regularity of $p$ -harmonic type systems below the critical growth. (Chinese) Acta Math. Sci. Ser. A Chin. Ed. 28 (2008), no. 3, 480–488. 

  58. Zheng, Shenzhou; Zheng, Xueliang; Feng, Zhaosheng Regularity for a class of degenerate elliptic equations with discontinuous coefficients under natural growth. J. Math. Anal. Appl. 346 (2008), no. 2, 359–373.

  59. Zheng, S.; Feng, Z. Regularity for quasi-linear elliptic systems with discontinuous coefficients. Dyn. Partial Differ. Equ. 5 (2008), no. 1, 87–99.

  60. Zheng, Shen Zhou Partial regularity for quasi-linear elliptic systems with VMO coefficients under the natural growth. (Chinese) Chinese Ann. Math. Ser. A 29 (2008), no. 1, 49--58; translation in Chinese J. Contemp. Math. 29 (2008), no. 1, 55–64 

  61. Zheng, Shenzhou; Zhang, Laping; Feng, Zhaosheng Everywhere regularity for $p$ -harmonic type systems under the subcritical growth. Commun. Pure Appl. Anal. 7 (2008), no. 1, 107–117.

  62. Zhao, Shu Le; Zheng, Shen Zhou $L^{2,\lambda}$ -regularity for a quasilinear elliptic equation with VMO coefficients. (Chinese) Acta Math. Sinica (Chin. Ser.) 50 (2007), no. 1, 17–24.

  63. Zheng, Shen Zhou; Zhao, Shu Le Regularity for $p$ -harmonic type systems with the gradients below the controllable growth. Acta Math. Sin. (Engl. Ser.) 22 (2006), no. 6, 1757–1766. 

  64. Zheng, Xue Liang; Zheng, Shen Zhou Another proof of the Lehtinen theorem. (Chinese) J. Shanghai Jiaotong Univ. (Chin. Ed.) 39 (2005), no. 10, 1737–1740. 

  65. Zheng, Shenzhou; Kang, Xiuying The comparison of Green function for quasi-linear elliptic equation. Acta Math. Sci. Ser. B Engl. Ed. 25 (2005), no. 3, 470–480. 

  66. Zheng, Shen Zhou The regularity of weakly quasiregular mappings in $\Bbb R^n$ . (Chinese) Chinese Ann. Math. Ser. A 25 (2004), no. 6, 799–804.

  67. Zheng, Shen Zhou Regularity results for the generalized Beltrami system. Acta Math. Sin. (Engl. Ser.) 20 (2004), no. 2, 293–304.

  68. Zheng, Shen-zhou Removable singularities of solutions of $A$ -harmonic type equations. Acta Math. Appl. Sin. Engl. Ser. 20 (2004), no. 1, 115–122.

  69. Zheng, Xue Liang; Zheng, Shen Zhou Riemann-Hilbert problem for N -analytic functions. (Chinese) J. Math. Study 34 (2001), no. 3, 292–297. 

  70. Zheng, Shen Zhou; Zheng, Xue Liang Bianalytic functions, biharmonic functions and elastic problems in the plane. Appl. Math. Mech. (English Ed.) 21 (2000), no. 8, 885–892; translated from Appl. Math. Mech. 21 (2000), no. 8, 797--802(Chinese)

  71. Zheng, Shen Zhou; Fang, Ai Nong Regularity of very weak solutions for a class of nonlinear elliptic systems. (Chinese) Acta Math. Sinica (Chin. Ser.) 42 (1999), no. 1, 119–124. 

  72. Zheng, Shenzhou Lp -integrability for p -quasiconformal homeomorphisms. J. Shanghai Jiaotong Univ. (Engl. Ed.) 3 (1998), no. 1, 10–13. 

  73. Zheng, Shenzhou; Fang, Ainong Regularity of very weak solutions for a class of nonlinear elliptic systems. Acta Math. Sinica (N.S.) 14 (1998), suppl., 733–740.  

  74. Zheng, Shen Zhou; Fang, Ai Nong Degenerate quasiregular mappings. (Chinese) Chinese Ann. Math. Ser. A 19 (1998), no. 6, 741–748. 

  75. Zheng, Shen Zhou; Fang, Ai Nong Lp -integrability of (K1,K2) -quasiregular mappings. (Chinese) Acta Math. Sinica (Chin. Ser.) 41 (1998), no. 5, 1019–1024. 

  76. Zheng, Shen Zhou (H,G) -transformations and quasiregular semigroups. (Chinese) J. Shanghai Jiaotong Univ. (Chin. Ed.) 32 (1998), no. 3, 116–119.  

  77.  Zheng, Shen Zhou Partial regularity of A -harmonic systems of equations and quasiregular mappings. (Chinese) Chinese Ann. Math. Ser. A 19 (1998), no. 1, 63--72; translation in Chinese J. Contemp. Math. 19 (1998), no. 1, 19–30.

  78. Zheng, Shenzhou On very weak solutions of nonlinear elliptic systems. J. Shanghai Jiaotong Univ. (Engl. Ed.) 2 (1997), no. 2, 6–11.   

  79. Zheng, Shen Zhou Beltrami systems with double characteristic matrices and quasiregular mappings. (Chinese) Acta Math. Sinica (Chin. Ser.) 40 (1997), no. 5, 745–750.

  80. Zheng, Xue Liang; Zheng, Shen Zhou Noether resolvability of systems of singular integral equations with conjugate terms. (Chinese) J. Changsha Univ. Electr. Power Nat. Sci. Ed. 12 (1997), no. 3, 251–256. 

  81. Nai, Bing; Zheng, Shen Zhou Displacement functions and Jørgensen's inequality in higher-dimensional spaces. (Chinese) J. Shanghai Jiaotong Univ. (Chin. Ed.) 31 (1997), no. 2, 16–19. 

  82. Zheng, Shen Zhou; Nai, Bing The Hölder continuity of (K,K′) quasiconformal mappings on Rn . (Chinese) J. Shanghai Jiaotong Univ. (Chin. Ed.) 31 (1997), no. 2, 13–15. 

  83. Zheng, Shen Zhou The theory of Noether solvability of systems of singular integral equations with shifts and complex conjugate values. (Chinese) J. Shanghai Jiaotong Univ. 30 (1996), suppl., 138–148. 

  84. Zheng, Shen Zhou Noether solvability and regularization of systems of singular integral equations with shifts. (Chinese) J. Shanghai Jiaotong Univ. 29 (1995), no. 5, 129–135.


多次得到国外知名大学和国际会议邀请报告:

  • Green functions of a class of degenerate operators with X-ellipticity. University of Texas Pan-American, Texas, USA, May,2008;
  • Remarks on approximate biharmonic maps to manifold. University of Kentucky,USA,March,2012;
  • Energy identity of approximate biharmonic maps and application. University of Texas Pan-AmericanUSAApril,2012;
  • Energy quantization for biharmonic maps to sphere. 9th AIMS Conference on Dynamical Systems, Differential Equations and Applications, Hyatt Grand Cypress, Orlando, Florida, USA, July, 2012.  



	

专著/译著

  1. 亓健,朱东鸣,郑神州. 高等数学(上下册)[M]. 国内:中国石油大学出版社, 2009-03
  2. 龚漫奇,邓小琴,郑神州,赵生变,王秋媛,缪克英,吴灵敏,黎传琦. 高等数学习题教程(上、下册)[M]. 科学出版社,2000-12

专利

软件著作权

获奖与荣誉

1998年北京市优秀青年骨干教师称号; 2014年参与的项目获铁道学会科技二等奖。

 

社会兼职

现为美国数学会《数学评论》(Mathematics Reviews)评论员,国内、外有关重要刊物和项目、基金评审专家,如评审高等院校科学技术奖、霍英东基金、国家自然基金等、中国博士后基金、博士点基金、北京市自然基金、浙江省自然基金等,专业刊物:Comm. PDE,Science in China等评审人.