西安交通大学 数学与统计学院

地址：西安市咸宁西路28号

邮编：710049

办公室：数学楼 204

办公电话：029-8266 6759

传真：029-8266 8551

电子信箱：zhangzc@mail.xjtu.edu.cn

School of Mathematics and Statistics

Xi'an Jiaotong University

28, West Xianning Road, Xi'an, Shaanxi

710049, P.R. China

Office Room: 204 Building of Mathematics

Office Tel: 86-29-8266 6759

Fax: 86-29-8266 8551 

• 2003， 西安交通大学，博士/Ph. D., Xi'an Jiaotong University

• 1997、2000， 河南师范大学，学士、硕士/B. S. & M. S., Henan Normal University

• 2016.1-7， 美国圣母大学，客座访问教授/Guest Visiting Professor, University of Notre Dame, 2016.1-7

• 2013-至今，西安交通大学，教授，博士生导师/Ph. D. supervisor, Professor, Xi'an Jiaotong University, 2013-present

• 2008-2009，美国圣母大学，访问学者/Visiting Scholar, University of Notre Dame, 2008-2009

• 2007-2012，西安交通大学，副教授/Associate Professor, Xi'an Jiaotong University, 2007-2012

• 2004-2007，西安交通大学，讲师/Lecturer, Xi'an Jiaotong University, 2004-2007
  

   

偏微分方程理论及其应用/Partial Differential Equations and their Applications

• In particular, I am interested in PDEs and their applications in Geometry, Physical mechanics, Fluid dynamics, Biology, Industry and Engineering, etc. A mathematical model of PDEs is an approximation of the real physical phenomenon for describing certain physical process, and it saves time and resources by analyzing the mathematical model rather than the underlying physical world. The physical world is very complicated, therefore, a good mathematical model should not include all the details of the problem, but rather, the model should be simple enough to capture some essential part of the problem and may provide some essential information for the real physical phenomenon.  

• For the PDE model, we study the local and global properties such as existence, uniqueness, regularity, asymptotic behavior, formation of singularities, and other special properties of the solutions. We use techniques such as foundamental elliptic and parabolic a priori estimates, fixed point theorems, variational argument, sub- and supersolution method, energy estimates, numerical computations and computer simulations.  

   

《数学物理方程》，《椭圆与抛物型方程》，《二阶椭圆型偏微分方程》，《二阶椭圆型方程与椭圆型方程组》，《二阶抛物型偏微分方程》，《变分法及其应用》，《非线性演化方程》，《抛物方程的爆破理论》，《非线性分析》，《应用数学基础》，《微分几何》，《张量分析》，《泛函分析》，《实变函数》，《复变函数》，《数学分析》，《高等代数与几何》等/ <Differential Equations in Mathematical Physics>, <Elliptic and Parabolic Partial Differential Equations>, <Elliptic Partial Differential Equations of Second Order>, <Second Order Elliptic Equations and Elliptic Systems>, <Parabolic Partial Differential Equations of Second Order>, <Variational Method and its Applications>, <Nonlinear Evolution Equations>, <Blow-up Theories for Semilinear Parabolic Equations>, <Nonlinear Analysis>, <Foundation of Applied Mathematics>, <Differential Geometry>, <Tensor Analysis>, <Functional Analysis>, <Real Function>, <Complex Function>, <Mathematical Analysis>, <Advanced Algebra and Geometry>, etc