首页 >> 教师名录

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:

    •  2017/11-2018/02  西班牙巴斯克应用数学中心合作研究项目,访问Luis Vega教授;
    •  2017/05-2017/07  西班牙巴斯克应用数学中心合作研究项目,访问Luis Vega教授(西班牙皇家科学院院士,欧洲科学院院士);   
    •  2013/07-2013/08  南开大学陈省身数学研究所, 访问教授;
    •  2011/09-2012/09  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

  • 主要研究方向: 偏微分方程理论及应用; 统计物理和金融数学模型及特殊函数; 共形、拟共形几何理论及应用; 量子场、色散方程的测不准原理。
  • 近期研究进展:(1)首次将格林函数应用于非线性偏微分方程的正则性研究, 克服了因非线性问题而造成格林函数和基本解应用的困境。 (2)证实Baricz关于修正Bessel函数商函数的严格对数凸性的猜想;解决了Hornik-Grun涉及特殊函数在参数(-1,-1/2)的公开问题。(3) 依据分层材料和电流变力学等物理背景,在弱条件下建立了一系列标准和非标准增长的椭圆和抛物方程问题广义Calderon-Zygmund型理论,使得该理论在多方面得到推进和拓展。(4)建立到Riemann流形上双调和映射能量的量子化,得到奇异点能量的有限泡泡过程; 当目标流形为球面时达到更优结果
  • 在国际知名刊物: Transactions of Amer. Math. Soc., Journal of Functional Analysis, Journal of Differential Equations, Manuscripta Math., 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., J. Inequal. Appl., Physica A 等发表了120余篇论文,其中SCI70篇,这些成果被国内外同行广泛参考和引用。

研究方向

  • 微分方程理论与应用
  • 非线性系统理论与应用

招生专业

  • 应用数学硕士
  • 系统理论硕士
  • 应用数学博士

科研项目

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

  • 田虹,郑神州.Lorentz estimate with a variable power for parabolic obstacle problems with non-standard growths.Journal of DifferentialEquations,2018,online(7)
  • 梁爽,郑神州.Global regularity in Lorentz spaces for nonlinear elliptic equations with Lp(·)logL-growth.Journal of Mathematical Analysis and Applications,2018,4(467)
  • 田虹,郑神州,Xiuying.Weighted Lorentz estimates for nonlinear elliptic obstacle problems with partially regular nonlinearities.Boundary Value Problems,2018,115(2018)
  • 张俊杰,郑神州.Lorentz estimates for asymptotically regular fully nonlinear parabolic equations.Mathematische Nachrichten,2018,5(291)
  • 张俊杰,郑神州.Weighted Lorentz and Lorentz–Morrey estimates to viscosity solutions of fully nonlinear elliptic equations.COMPLEX VARIABLES AND ELLIPTIC EQUATIONS,2018,9(63)
  • 梁爽,郑神州.On W1, γ (·)-regularity for nonlinear non-uniformly elliptic equations.manuscripta math,2018,online(7)
  • 王倚端,郑神州,张伟,王国超,王军.Fuzzy entropy complexity and multifractal behavior of statistical physics financial dynamics.Physica A,2018,3(506)
  • 李惠珍,张俊杰,郑神州.Orlicz estimates for nondivergence linear elliptic equations with partially BMO coefficients.Complex Variables and Elliptic Equations,2018,6(63)
  • 梁爽,郑神州.Variable Lorentz estimate for nonlinear elliptic equations with partially regular nonlinearities.Nonlinear Analysis,2018,1(172)
  • 张俊杰,郑神州.Lorentz estimates for asymptotically regular fully nonlinear parabolic equations.Mathematische Nachrichten.,2018,5(291)
  • Hang,郑神州.Monotonicity of the ratio of modified Bessel functions of the first kind with applications.Journal of Inequalities and Applications,2018,2018(57)
  • Hang,郑神州.MONOTONICITY AND CONVEXITY OF THE RATIOS OF THE FIRST KIND MODIFIED BESSEL FUNCTIONS AND APPLICATIONS.Mathematical Inequalities & Applications,2018,1(21)
  • 李习桥,刘志明,Hang,郑神州.Sharp Smith’s bounds for the gamma function.Journal of Inequalities and Applications,2018,27(2018)
  • 王倚端,郑神州,张伟,王军,王国超.Modeling and complexity of stochastic interacting Lévy type financial price dynamics.Physica A,2018,499(2)
  • 梁爽,郑神州.GRADIENT ESTIMATE IN ORLICZ SPACES FOR ELLIPTIC OBSTACLE PROBLEMS WITH PARTIALLY BMO NONLINEARITIES.Electronic Journal of Di fferential Equations,2017,58(2018)
  • 于海燕,郑神州.拟线性次椭圆方程组在Morrey空间上的部分正则性.数学年刊A辑(中文版),2017,38A(4)
  • 于海燕,郑神州.Partial Regularity in Morrey Spaces for Quasi-linear Subelliptic Systems.Chinese Journal of Contemporary Mathematics,,2017,38(4)
  • 田虹,郑神州.Uniformly nondegenerate elliptic equations with partially BMO coefficients in nonsmooth domains.Nonlinear Analysis,2017,156(1)
  • Hang,郑神州.Complete monotonicity involving some ratios of gamma functions.Journal of Inequalities and Applications,2017,255(2017)
  • Hang,郑神州.MONOTONICITY AND CONVEXITY OF THE RATIOS OF THE FIRST KIND MODIFIED BESSEL FUNCTIONS AND APPLICATIONS.Mathematical Inequalities & Applications,2017,1(21)
  • 王倚端,郑神州,张伟,王军.Complex and Entropy of Fluctuations of Agent-Based Interacting Financial Dynamics with Random Jump.Entropy,2017,19(512)
  • 田虹,郑神州.Lorentz estimates for the gradient of weak solutions to elliptic obstacle problems with partially BMO coefficients.Boundary Value Problems,2017,2017(128)
  • 张俊杰,郑神州.Weighted Lorentz and Lorentz–Morrey estimates to viscosity solutions of fully nonlinear elliptic equations.Complex Variables and Elliptic Equations,2017,2017(8)
  • 田虹,郑神州.Global weighted Lorentz estimates to nonlinear parabolic equations over nonsmooth domains.J. Math.Anal.Appl.,2017,456(8)
  • 李惠珍,张俊杰,郑神州.Orlicz estimates for nondivergence linear elliptic equations with partially BMO coefficients.Complex Variables and Elliptic Equations,2017,62(8)
  • Yang,郑神州.Sharp Bounds for the Ratio of Modified Bessel Functions.Mediterr. J. Math,2017,14(169)
  • 骆天琪,吕慧琳,Yang,郑神州.New Sharp Approximations Involving Incomplete Gamma Functions.Results Math,2017,72(1-2)
  • 张俊杰,郑神州.Lorentz estimates for fully nonlinear parabolic and elliptic.Nonlinear Analysis,2017,148(2)
  • 王勇勇,张俊杰,郑神州.LORENTZ ESTIMATES FOR ASYMPTOTICALLY REGULAR FULLY NONLINEAR ELLIPTIC EQUATIONS.Electronic Journal of Differential Equations,,2017,2017(120)
  • 吕慧琳,Hang,骆天琪,郑神州.Sharp inequalities for tangent function with applications.Journal of Inequalities and Applications,2017,2017(94)
  • YANG,郑神州.THE MONOTONICITY AND CONVEXITY FOR THE RATIOS OF MODIFIED BESSEL FUNCTIONS OF THE SECOND KIND AND APPLICATIONS.PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY,2017,7(145)
  • 张俊杰,郑神州.WEIGHTED LORENTZ ESTIMATES FOR NONDIVERGENCE LINEAR ELLIPTIC EQUATIONS WITH PARTIALLY BMO COEFFICIENTS.COMMUNICATIONS ON PURE AND APPLIED ANALYSIS,2016,16(3)
  • 于海燕,王洁,郑神州.自然增长下次椭圆 A-调和方程的Holder}连续性估计.应用数学学报,2016,5(39)
  • 张俊杰,郑神州.Lorentz estimates for fully nonlinear parabolic and elliptic equation.Nonlinear Analysis,2016,10(148)
  • Yang,郑神州.Monotonicity of a mean related to polygamma functions with an application.Journal of Inequalities and Applications,2016,216(2016)
  • 孙帮成,刘志明,李强,郑神州.Lp-Estimates for quasilinear subelliptic equations with VMO coefficients under the controllable growth.Boundary Value Problems,2016,148 (2016)
  • 郑神州,郑学良,zhaosheng.Regularity for a class of degenerate elliptic equations with discontinuouscoefficients under natural growth .J. Math. Anal. Appl.,2008,6(346)
  • 孙帮成,刘志明,李强,郑神州.The monotonicity and convexity of a function involving psi function with applications.Journal of Inequalities and Applications,2016,151(2016)
  • 张俊杰,郑神州.LORENTZ ESTIMATES FOR ASYMPTOTICALLY REGULAR ELLIPTIC EQUATIONS IN QUASICONVEX DOMAINS.Electronic Journal of Dierential Equations,2016,145(2016)
  • 于海燕,郑神州,佟玉霞.An alternative approach to partial regularity of quasilinear elliptic systems with VMO coefficients.Journal of Inequalities and Applications,2016,2016(20)
  • 于海燕,郑神州.MORREY ESTIMATES FOR SUBELLIPTIC p-LAPLACE TYPE SYSTEMS WITH VMO COEFFICIENTS IN CARNOT GROUPS .Electronic Journal of Dierential Equations,2016,33(2016)
  • 张俊杰,郑神州.Lorentz estimate for nonlinear parabolic obstacle problems with asymptotically regular nonlinearities .Nonlinear Analysis,2016,1(134)
  • 郑神州.A COMPACTNESS RESULT FOR POLYHARMONIC MAPS IN THE CRITICAL DIMENSION .Czechoslovak Mathematical Journal,2016,141(66)
  • Cheng,Li,Wang,郑神州.Traveling Waves Connecting Equilibrium and Periodic Orbit for a Delayed Population Model on a Two-Dimensional Spatial Lattice.International Journal of Bifurcation and Chaos,2016,3(26)
  • 郑神州.A Local H\"older Estimate of (K1,K2)-Quasiconformal Mappings between Hypersurfaces.Acta Mathematica Sinica, English Series,2015, No. 9(Vol. 31)
  • 郑神州.A strong convergence of the weak gradient to A-harmonic type operators with L1data.Journal of Mathematical Analysis and Applications,2015, No.5(Vol.430)
  • 郑神州,Feng.Regularity of subelliptic p-harmonicsystems withsubcritical growth in Carnot group.J. DifferentialEquations,2015,No.3(Vol.258)
  • 于海燕,郑神州.OPTIMAL PARTIAL REGULARITY FOR QUASILINEAR ELLIPTIC SYSTEMS WITH VMO COEFFICIENTS BASED ON A-HARMONIC APPROXIMATIONS.Electronic Journal of Differential Equations,2015,No.16(Vol.2015)
  • 于海燕,郑神州.BMO estimate to A-harmonic systems with discontinuous coefficients.Nonlinear Analysis: Real World Applications,2015,No.5(Vol.26)
  • 张晋杰,郑神州.On refined Hardy-Knopp type inequalities in Orlicz spaces and some related results.Journal of Inequalities and Applications,2015,No.169(Vol.2015)
  • 佟玉霞,郑神州,于海燕.变指数A-调和方程弱解梯度H\"older连续性.数学物理学报,2015,No.4(Vol.35A)
  • 王洁,于海燕,郑神州.自然增长的半线性次椭圆方程内部H\"older连续性.数学物理学报,2014,34A(6)
  • 佟玉霞,郑神州,Jiantao.Higher Integrability for Very Weak Solutions of Inhomogeneous .Journal of Applied Mathematics,2014,2014(Article ID 308751)
  • 佟玉霞,Jiantao,郑神州.Zeros for the Gradients of Weakly A-Harmonic Tensors.Journal of Applied Mathematics,2014,2014(Article ID 231248)
  • 郑神州,Z.Regularity for Quasi-linear Elliptic Systems with Discontinuous Coecients.Dynamics of PDE,2014,5(1)
  • 郑神州.ENERGY QUANTIZATION FOR APPROXIMATE H-SURFACES AND APPLICATIONS.Electronic Journal of Dierential Equations,2013,117(2013)
  • 饶婕晟,郑神州.Heisenberg群上拟正则映射正则性的改进.数学年刊,2013,3(34)
  • 郑神州.具间断系数拟线性退化椭圆方程在可控增长下的正则性.系统科学与数学,2012,5(32)
  • 郑神州,卢寒芳.次椭圆拟线性方程在外区域上的Liouville定理.数学物理学报,2012,4(32A)
  • Wang,郑神州.ENERGY IDENTITY FOR A CLASS OF APPROXIMATE BIHARMONIC MAPS INTO SPHERE IN DIMENSION FOUR.DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS,2013,2(33)
  • Feng,Tian,郑神州,卢寒芳.Travelling wave solutions of the Burgers–Huxley equation.IMA Journal of Applied Mathematics,2012,6(77)
  • 郑神州,Feng.GREEN FUNCTIONS FOR A CLASS OF NONLINEAR DEGENERATE OPERATORS WITH X-ELLIPTICITY.TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY,2012,7(364)
  • Wang,郑神州.Energy identity of approximate biharmonic maps to Riemannian manifolds and its application.Journal of Functional Analysis,2012,4(263)
  • 郑神州.WEAK COMPACTNESS OF BIHARMONIC MAPS.Electronic Journal of Differential Equations,2012,190(2012)
  • 郑神州,Zheng,Feng.Optimal Regularity for $A$-Harmonic Type Equations.DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS SERIES B,2011,No.2(Vol.16)
  • Gao,郑神州.Beltrami System with Two Characteristic Matrices and Variables Coefficients.Proceedings of the Third International Conference,2011
  • 郑神州,卢寒芳.X-椭圆方程弱解内部H\.数学年刊,2010,3(30A)
  • 郑神州,王喜芬.拟线性次椭圆方程很弱解的正则性.数学物理学报,2010,2(30)
  • 王春华,郑神州.一类具间断系数退化椭圆型方程的$L^{p,\lambda}$正则性.系统科学与数学,2010,2(30)
  • Wang Yuandi,郑神州."The Existence and Behavior of Solutions for."Hindawi Publishing Corporation,2009,无(Vol.2009)
  • Feng ZS,郑神州.Traveling wave solutions to a reaction-di®usion equation.Z. angew. Math. Phys.,2009,0(Vol.60)
  • 卢寒芳,郑神州.散度型椭圆方程Holder连续性的Green函数法.数学物理学报,2009,No. 5(Vol. 29)
  • 卢寒芳,郑神州.具有特征矩阵的退化椭圆方程外边值问题.北京交通大学学报,2008,3(32)
  • 郑神州,赵书乐.低于临界增长p-调和方程组的完全正则性.数学物理学报,2008,3(28A)
  • 郑学良,郑神州.自然增长下非线性退化椭圆方程的优化Holder连续指数.数学学报,2008,4(51)
  • 郑神州.自然增长下具VMO系数拟线性椭圆组的部分正则性.数学年刊,2008,1(29A)
  • 郑神州,章腊萍.次临界增长p-调和组的处处内部正则性.数学学报,2008,5(51)
  • 郑神州.Partial regularity for quasilinear elliptic systems under the natural growth.Chin.J.Contem.Math.,2008,1(29)
  • 郑神州.Regularity for quasilinear degenerate elliptic equations with VMO coefficients.Acta Math.Sinica,2008,11(24)
  • 赵书乐,郑神州.具有VMO系数的拟线性椭圆方程的L2,λ.数学学报(中文版),2007,1(50)
  • 王占,郑神州.一类非齐次A-调和方程很弱解的唯一性.北京交通大学学报,2007,3(31)
  • 王定龙,王占,郑神州.一类退化椭圆型方程很弱解得正则性和稳定性.北京交通大学学报,2007,6(31)
  • 王春华,郑神州.具有VMO微线性椭圆方程组的部分正则性.北京交通大学学报,2006,6(30)
  • 郑神州,赵书乐.Regularity for P-Harmonic Type Systems with the Gradients below the Controllable Growth.Acta Mathematica Sinica,English Series,2006,6(22)
  • 郑神州,渠刚荣.N-解析函数类中的复合型边值问题.北方交通大学学报,2001,3(25)
  • 郑神州,郑学君.双解析函数.双调和函数和平面弹性问题.应用数学学报,2000,8(21)
  • 郑神州,郑学君.Biandytic functions,Bcharmic functions and Elastic problems in the plane.Applied Mathemects and Mechamis,2000,8(21)
  • 郑神州,郑学君.Liouville定理的另一种证明.北方交通大学学报,2000,8(24)
  • 郑神州,方爱农.一类非线性椭圆组很弱解的正则性.数学学报,1999,1()
  • 翟小云,郑神州.一类非齐次退化椭圆方程组的C1,α正则性.北方交通大学学报,2004,3(28)
  • 郑神州,郑学良.Riemann-Hilbert’s boundary value problem for N-analytic functions.Proceedings of the Eighth International Colloquium on Complex Analysis,2000,2001
  • 郑神州.Riemann-Hilbert Boundary Value Problem for N-Analytic Functions."Finite or Infinite Dimensional Complex Analysis"(2000),2000
  • 郑神州.Removable Singularities of Solutions of A-harmonic Type Equations.Acta Mathematica Sinica,English Series,2004,1(20)
  • 郑神州,郑学良.拟正则映射和变分关系.北方交通大学学报,1999,2(23)
  • 郑神州.周期Haseman问题的保角粘合映射方法.北京交通大学学报,2004,?(12)
  • 郑神州.弱拟正则映射的正则性.数学年刊,2004,?(12)
  • 郑神州.N解析函数和一类奇异位分——积分方程.北方交通大学学报,2003,3(27)
  • 郑神州.Regularity Results for the Generalized Beltrami System.Acta Mathematica Sinica,English Series,2004,1(20)
  • 郑神州,康秀英.The comparison of green function for quasi-linear elliptic equation.Acta Mathematica Scientia,2005,3(25B)

专著/译著

  • 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
  • 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年参加的项目< 动车组检修计划优化关键技术及应用>获中国铁道学会科技二等奖

 

社会兼职

  • 美国数学会《数学评论》(Mathematics Reviews)评论员;
  • 国家自然科学基金项目、高等院校科学技术奖、霍英东基金、国家自然基金、中国博士后基金、博士点基金、北京市自然基金、浙江省自然基金等网评专家;  
  • 教育部学位办博、硕士学位论文通讯评论专家;
  • 专业国际知名期刊如:Commun. Part. Diff. Equ.,Commun. Nonlinear Sci. Numer. Simulat., JMAA, Science in China等评审专家.