基本信息

韩丕功 男 博导 数学与系统科学研究院
电子邮件:pghan@amss.ac.cn
通信地址:北京海淀区中关村东路55号中科院数学院
邮政编码:100190

研究领域

主要从事非线性偏微分方程和流体力学问题的研究;应用非线性分析来研究偏微分方程解的存在性,多解性等;利用Fourier 分析和半群理论研究不可压缩Navier-Stokes 方程解的正则性和大时间行为。

招生信息

   
招生专业
070104-应用数学
招生方向
非线性偏微分方程

教育背景

2001-09--2004-07 中国科学院数学与系统科学研究院 博士学位
学历

-- 博士研究生

学位
-- 博士

工作经历

2012年 2月被中国科学院数学与系统科学研究院聘为研究员

2007年 3月被中国科学院数学与系统科学研究院聘为副研究员   

2004年 7月被中国科学院数学与系统科学研究院聘为助理研究员   

2004年 7月在中国科学院数学与系统科学研究院获理学博士学位
工作简历
   
社会兼职
   

教授课程

偏微分方程概论

专利与奖励

2006年荣获全国百篇优秀博士学位论文奖   

2010年荣获中国科学院卢嘉锡青年人才奖 

2011年荣获中国科学院数学院优秀教师奖
奖励信息
(1) 中国科学院卢嘉锡青年人才奖,院级级,2010
(2) 全国百篇优秀博士学位论文奖,部委级,2006
专利成果
   

出版信息

1. Pigong Han and Zhaoxia Liu, Positive Solutions for Elliptic Equations Involving Critical Sobolev Exponents and Hardy Terms with Neumann Boundary Conditions, Nonlinear Analysis, 55 (2003) 167-186.   

2. Daomin Cao and Pigong Han, A Note on the Positive Energy Solutions for Elliptic Equations Involving Critical Sobolev Exponents, Applied Mathematics Letters, 16 (2003) 1105-1113.   

3. Daomin Cao and Pigong Han, Multiple Positive Solutions of Nonhomogeneous Elliptic Systems with Strongly Indefinite Structure and Critical Sobolev Exponents, Journal of Mathematical Analysis and Applications, 289 (2004) 200-215.   

4. Pigong Han and Zhaoxia Liu, The Sign-changing Solutions for Singular Critical Growth Semilinear Elliptic Equations, Differential and Integral Equations, 17 (2004) 835-848.   

5. Daomin Cao and Pigong Han, Solutions for Semilinear Elliptic Equations with Critical Exponents and Hardy Potential, Journal of Differential Equations, 205 (2004) 521-537.   

6. Pigong Han, Strongly Indefinite Systems with Critical Sobolev Exponents and Weights,Applied Mathematics Letters, 17 (2004) 909-917.   

7. Pigong Han and Zhaoxia Liu, Multiple Positive Solutions of Strongly Indefinite Systems with Critical Sobolev Exponents and Data That Change Sign, Nonlinear Analysis, 58 (2004) 229-243.   

8. Junning Zhao and Pigong Han, BV Solutions of Dirichlet Problem for a Class of Doubly Nonlinear Degenerate Parabolic Equations. Journal of Partial Differential Equations, 17 (2004) 241--254.   

9. Pigong Han, Quasilinear Elliptic Problems with Critical Exponents and Hardy Terms, Nonlinear Analysis, 61 (2005) 735-758.   

10. Pigong Han, The Dirichlet problem for a class of nonlinear degenerate parabolic equations. Journal of Inequalities and Applications, 9 (2005) 395--402.

11. Pigong Han, High Energy Positive Solutions for a Critical Growth Dirichlet Problem in Noncontractible Domains, Nonlinear Analysis, 60 (2005) 369-387.   

12. Daomin Cao and Pigong Han, High Energy Positive Solutions of Neumann Problems for an Elliptic System of Equations with Critical Nonlinearities, Calculus of Variations and Partial Differential Equations, 25 (2005) 161-185.   

13. Pigong Han, Existence of solutions for semilinear elliptic equations involving critical Sobolev exponents and Hardy terms. Acta Mathematica Scientia, 25 (2005) 533--544.   

14. Pigong Han, Solutions for Singular Critical Growth Schrodinger Equations with Magnetic Field, Portugaliae Mathematica, 63 (2006) 37--45.   

15. Pigong Han, Multiple Positive Solutions of Nonhomogeneous Elliptic Systems Involving Critical Sobolev Exponents, Nonlinear Analysis, 64 (2006) 869-886.   

16. Pigong Han, Multiple Positive Solutions for a Critical Growth Problem with Hardy Potential, Proceedings of the Edinburgh Mathematical Society, 49 (2006) 53-69.   

17. Daomin Cao and Pigong Han, Solutions to Critical Elliptic Equations with Multi-Singular Inverse Square Potentials, Journal of Differential Equations, 224 (2006) 332-372.   

18. Pigong Han, The Effect of the Domain Topology on the Number of Positive Solutions of an Elliptic System Involving Critical Sobolev Exponents, Houston Journal of Mathematics, 32 (2006), no. 4, 1241–1257 .   

19. Pigong Han, Asymptotic Behavior of Solutions to Semilinear Elliptic Equations with Hardy Potential, Proceedings of the American Mathematical Society, 135 (2007), no. 2, 365–372 .   

20. Pigong Han, Multiple Solutions to Singular Critical Elliptic Equations, Israel Journal of Mathematics, 156 (2006), 359–380.   

21. Pigong Han and Zhaoxia Liu, Solutions for a singular critical growth problem with a weight. J. Math. Anal. Appl. 327 (2007), no. 2, 1075–1085.   

22. Pigong Han and Zhaoxia Liu, On a class of critical heat equations with an inverse square potential. Differential Integral Equations 20 (2007), no. 1, 27–50.   

23. Pigong Han and Zhaoxia Liu, Solutions to nonlinear Neumann problems with an inverse square potential. Calc. Var. Partial Differential Equations 30 (2007), no. 3, 315–352.   

24. Pigong Han, Many solutions for elliptic equations with critical exponents. Israel J. Math. 164 (2008), 125–152.   

25. Zhaoxia Liu and Pigong Han, Asymptotic behaviour of positive solutions for critical systems with strongly indefinite structure. Appl. Anal. 87 (2008), no. 3, 363–376.   

26. Zhaoxia Liu and Pigong Han, Existence of solutions for singular elliptic systems with critical exponents. Nonlinear Anal. 69 (2008), no. 9, 2968–2983.   

27. Zhaoxia Liu and Pigong Han, Infinitely many solutions for elliptic systems with critical exponents. J. Math. Anal. Appl. 353 (2009), no. 2, 544–552.   

28. Pigong Han, Regularity and decay properties of weak solutions to Navier-Stokes equations in general domains. Port. Math. 67 (2010), no. 1, 57–74.   

29. Pigong Han, Regularity of weak solutions to 3D incompressible Navier-Stokes equations. J. Evol. Equ. 10 (2010), no. 1, 195–204.   

30. Pigong Han, Asymptotic behavior for the Stokes flow and Navier-Stokes equations in half spaces. J. Differential Equations 249 (2010), no. 8, 1817–1852.   

31. Daomin Cao and Pigong Han, Inhomogeneous critical nonlinear Schrodinger equations with a harmonic potential. J. Math. Phys. 51 (2010), no. 4, 043505, 24 pp.   

32. Pigong Han, Decay results of solutions to the incompressible Navier–Stokes flows in a half space. J. Differential Equations. 250 (2011), no. 10, 3937–3959. 

33. Pigong Han,  Large time behavior for the incompressible  Navier–Stokes flows in 2D exterior domains. Manuscripta Math. 138 (2012) , no, 3, 347–370.

34. Pigong Han, Algebraic L^2 decay for weak solutions of a viscous Boussinesq system in exterior domains. J. Differential Equations. 252 (2012), 6306–6323.

35. Pigong Han, Global well-posedness and scattering for the focusing nonlinear Schrodinger equation in the nonradial case.  Opuscula Math. 32  (2012) 487--504.

36. Pigong Han, Weighted decay properties for the incompressible Stokes flow and Navier-Stokes equations in a half space. J. Differential Equations. DOI: 10.1016/j.jde.2012.06.007.

发表论文
(1) Journal of Differential Equations,2011,第1作者
(2) Journal of Evolution Equations,2010,第1作者
(3) Port. Math,2010,第1作者
(4) Journal of Differential Equations,2010,第1作者
(5) Journal of Mathematical Physics,2010,第2作者
发表著作
   

科研活动

在研项目:不可压缩Navier-Stokes方程中的一些问题;2011.1~~2013.12
科研项目
(1) 不可压缩Navier-Stokes方程中的一些问题,主持,国家级,2011-01--2013-12
参与会议
   

合作情况

   
项目协作单位
   

指导学生

现指导学生

朱逸  硕士研究生  070104-应用数学  

宋婧  硕士研究生  070104-应用数学