曹道民

作者: 时间:2017-07-10 点击数:

一、基本信息

 

曹道民教授

 

研究领域:非线性偏微分方程和非线性分析

 

办公地点:行政西楼前座330

 

办公电话:020-39366860

 

电子邮箱:dmcao@amt.ac.cn

 

 

二、个人简介

曹道民,男,1963年出生, 现为广州大学数学与信息科学院院长。

主要从事非线性偏微分方程和非线性分析的研究,共发表论文100多篇,专著一部,大多数论文发表在国际知名期刊上。曾获国家杰出青年基金(2004年)和中国科学院青年科学家奖(1999年),曾任中国科学院数学与系统科学研究院应用数学研究所所长。多次承担国家自然科学基金重点项目和面上项目,主持了中国科学院知识创新工程重要方向性项目《数学物理中的若干重大问题》和中国科学院前沿项目《带间断非线性椭圆型方程》。现任《应用数学学报》和《数学物理学报》副主编,是《Applicable Analysis》、《Annales Academiae Scientiarum Fennicae, Mathematica》等多种刊物的编委。

已指导毕业博士研究生18人,他们中有国家杰出青年基金获得者、全国百

篇优秀博士论文获得者,多人获德国洪堡基金会的资助(Humbodlt Research Fellowship )或日本学术振兴会(JSPS)的资助.

 

三、教育背景

1. 1986/9 - 1989/6,中国科学院系统科学研究所(现中国科学院数学与系统科学研究院),博士,

2. 1983/9 - 1986/6,湖南省湘潭大学,数学系,硕士,

3. 1979/9 - 1983/6,湖南省湘潭大学,数学系,学士

 

四、职业经历

1. 2017/4 - 至今,广州大学数学与信息学院,教授

2. 1997/10 – 2017.3,中国科学院数学与系统科学研究院,应用数学研究所,研究员

3. 1993/1 - 1997/9,中国科学院武汉物理与数学研究所,研究员

4. 1991/1 - 1992/12,中国科学院武汉数学物理研究所,副研究员

1989/6 - 1991/12,中国科学院武汉数学物理研究所,助理研究员

 

五、主要学术访问

1. 2018/7-2018/8: 美国华盛顿大学数学系,访问教授;

2. 2012/10-2012/4: 德国吉森(Gissen)大学数学系,访问教授;

3. 2011/8-2011/9: 受芬兰科学院资助,在芬兰屈瓦斯古那(Jyvaskyla)大学数学系访问,访问教授;

4. 2010/3: 美国鲁特季斯(Rutgers)大学数学系,访问教授;

5. 2007/10-2007/11: 澳大利亚昆士兰大学(The University of Queensland)做访问教授;

6. 2004/5-2004/6: 瑞士洛桑高工(Ecole Polytechnique Federale de Lausanne (EPFL), Switzerland)做访问教授;

7. 2001/6-2001/8: 澳大利亚新南威尔士大学(The University of New South Wales)做访问教授;

8. 1996/5-1997/6: 受德国洪堡基金会(A.von Humboldt Foundation)资助,在德国科隆大学和美因兹大学做洪堡学者(Humboldt Research Fellowship);

9. 1995/6--Aug.1995/8: 澳大利亚新南威尔士大学(The University of New South Wales)做访问学者;

10. 1991/8-1992/7: 受王宽成基金会资助在法国第九大学(Universite de Paris–Dauphine)做访问学者

 

六、 教授课程

1. 本科生课程:数学分析,解析几何

2. 研究生课程:偏微分方程,非线性分析

 

七、奖励与荣誉

1. 1991年 项目“无界域上非线性椭圆型方程研究”获中国科学院自然科学奖二等奖, 颁奖单位:中国科学院

2.1992年10月获国务院颁发的政府特殊津贴, 证书编号:政府特殊津贴第(92)4911862号,授予单位: 中华人民共和国国务院

3.1996年获武汉市市管中青年优秀专家称号, 证书编号: (96)9890011, 颁证单位,中共武汉市委员会,武汉市人民政府,

4.1999年获教育部科学技术进步奖三等奖, 颁奖单位:教育部

5. 1999 年 中国科学院青年科学家奖一等奖(个人),颁奖单位:中国科学院

6. 2000年 项目“非线性椭圆型方程解的存在性及其性质研究”获湖北省自然科学奖二等奖,奖证编号: 2000Z-040-2-016-001-R02, 颁奖单位:湖北省人民政府

7. 2000年 中国科学院杰出青年(个人), 授予单位:中国科学院

8. 2004年 新世纪百千万人才工程国家级人选, 证书编号:第04-491008号,颁证单位:中华人民共和国人事部

9. 2004年 中国科学院优秀研究生导师奖,颁奖单位:中国科学院

10.2005年 中国科学院优秀研究生指导教师奖,颁奖单位:中国科学院

11.2006年中国科学院研究生院优秀研究生导师奖,颁奖单位:中国科学院

 

八、科研服务

主持或参加的在研科研项目(课题)

1. 国家自然科学基金重点项目,批准号11831009,非光滑变分理论及其在椭圆型偏微分方程中的应用, 参与, 2019/01-2023/12

2. 中国科学院前沿科学重点研究项目,带间断的非线性偏微分方程, 主持,2017/01-2021/12

 

以前主持或参加的部分科研项目(课题)

1. 国家自然科学基金重点项目,批准号11331010,现代变分问题的若干问题

研究,2014/01-2018/12,已结题,参与。

2. 国家自然科学基金面上项目,批准号11271354,带间断非线性项椭圆型偏

微分方程,2013/01-2016/12,已结题,主持

3. 国家自然科学基金重点项目,批准号10631030,非线性椭圆与抛物型方程

的理论及其应用研究,2007/01-2010/12,已结题,参加

4. 中国科学院知识创新工程重要方向性项目《数学物理中的若干重大问题》,

2007/01-2009/12,已结题,主持

5. 973 项目“数学与其它领域交叉的若干专题”子课题《流体力学与材料科

学中的偏微分方程》,2006/01-2010/12,参加,骨干成员

6. 国家自然科学基金杰出青年基金项目, 批准号10425104,非线性偏微分方

程,2005/01-2008/12,已结题,主持

7. 973项目“核心数学的若干前沿问题”子项目《非线性偏微分方程》,

G1990751,1999/01-2004/12,已结题,参加

8. 国家自然科学基金项目面上项目, 批准号19871091,非线性椭圆型方程的多

峰解,1998/01- 2001/12,已结题,主持

9. 中科院“百人计划”,1997/01-1999/12,已结题,主持。

 

九、研究成果

近年发表的论著

论文

[1] Nodal solutions for a supercritical semilinear problem with variable exponent, Calc. Var. Partial Differential Equations, 57 (2018), (with Li Shuanglong and Liu Zhongyuan)

[2] Sign-changing bubble tower solutions for the supercritical Hénon-type equations, Ann. Mat. Pura. Appl. 197(2018),1227–1246. (with Zhongyuan Liu and Shuangjie Peng)

[3] Steady vortex patches with opposite rotation directions in a planar ideal fluid,Calculus of Variations and Partial Differential Equations, 58(2019) 58:75 (with Guodong Wang)

[4] Steady vortex patch solutions to the vortex-wave system,Nonlinearity,32(2019),1182-1904(with Guodong Wang)

[5] Nonlinear orbital stability for planar vortex patches, Proceedings of the American Mathematical Society,147(2019),775-784. (with Jie Wan and Guodong Wang)

[6] Classification of nonnegative solutions to a bi-harmonic equation with Hartree type nonlinearity, Proceedings of the Royal Society of Edinburgh, 149(2019),979-994. (with Wei Dai)

[7] Local uniqueness for vortex patch problem in incompressible planar steady flow, Journal de Mathématiques Pures et Appliquées,131(2019), 251-289.(with Yuxia Guo, Shuangjie Peng and Shusen Yan)

[8] A note steady vortex flows in two dimensions, Proc. Amer. Math. Soc., 128(2020), 1153-1159. (with Guodong Wang)

[9] Steady vortex patch with polygonal symmetry for the planar Euler equations in a disc, Nonlinear Analysis: Real World Applications, 51(2020),103008. (with Guodong Wang)

[10] On the ground state of fractional spinor Bose-Einstein condensates, Advances in Differential Equations, 25(2020), 105–134. (with Jinchun He, Haoyuan Xu and Meihua Yang)

 

专著

《Singularly Perturbed Method for Nonlinear Elliptic Problem》(与彭双阶、严树森合著),Cambridge University Press,2020

 

以前发表的部分论文

[1] On the existence and nodal character of solutions of semilinear

elliptic equations, Acta Mathematica Scientia, 8(1988),345-395.(with Zhu Xiping)

[2] The concentration-compactness principle in nonlinear elliptic

equations, Acta Mathematica Scientia},9(1989),307-323.(with Zhu Xiping)

[3] Bifurcation for quasilinear equations on RN with natural growth conditions, Proc. Royal Soc. Edinburgh, 113A(1989), 215-228.(with G.Li and S.Yan)

[4] Positive solutions and bifurcation from the essential spectrum

of a semilinear elliptic equation on RN, Nonlinear Analysis,TMA, 15(1990), 1045-1052.

[5] Bifurcation for quasilinear elliptic system on RN with natural growth conditions, J. London Math.Soc., 44(1991),514-524.

[6] Nontrivial solutions of semilinear elliptic equations with critical exponent in R2, Comm. Part. Diff. Equat., 17(1992), 407-435.

[7] Multiple solutions of a Neumann problem in an exterior domain, Comm. Part. Diff. Equat., 18(1993), 687-700.

[8] Multiple solutions of a semilinear elliptic equation on RN,

Ann. Inst. H. Poincare, Anal. Non lineaire, 10(1993), 593-604.

[9] Multiple solutions of inhomogeneous elliptic equations involving

critical Sobolev exponent, Proc. Royal Soc.Edinburgh, 124A(1994), 1177-1191.(with G.Li and H.Zhou)

[10] Multiple positive and nodal solutions for semilinear elliptic

equations involving critical Sobolev exponents, Indiana Univ.Math. J., 44(1995), 1249-1271.(with E.S.Noussair)

[11] On the existence of multiple solutions of nonhomogeneous equations involving critical Sobolev exponent, Z. Angew. Math. Phys, 47(1996), 89-96.(with H.Zhou)

[12] Multiplicity of positive and nodal solutions for nonlinear elliptic problems, Ann. Inst.H. Poincare, Anal. Nonlineaire, 13(1996), 557-588. (with E.S.Noussair)

[13] On the existence and profile of multi-peaked solutions to singularly perturbed semilinear Dirichlet problems, Discrete and Continuous Dynamical System, 2(1996), 221-236.(with E.N.Dancer, E.S.Noussair and S.Yan)

[14] Existence and uniqueness results on single-peaked solutions of a semilinear problem, Ann. Inst. H.Poincare, Anal. Non lineaire, 15(1998), 73-111.(with E.S.Noussair and S.Yan)

[15] On the existence of multi-peaked solutions to a semilinear Neumann problem, Duke Math. J.,97(1999), 261-300.(with T.Kupper)

[16] Solutions with multiple "peaks" for nonlinear elliptic equations, Proc.Royal Soc.Edinburgh,126A(1999), 235-264.(with E.S.Noussair and S.Yan)

[17] Multi-peak solutions for a singularly perturbed semilinear elliptic problem,J.Diff. Equat.,166(2000), 266-289.(with E.S.Noussair)

[18] Existence of symmetric multi- peaked solutions to singularly perturbed semilinear problems, Comm. Part .Diff. Equat., 25(2000), 2185-2232.(with E.S.Noussair)

[19] Existence and nonexistence of interior-peaked solution for a nonlinear Neumann problem, Pacific J.Math.,200(2001), 19-40.(with E.S.Noussair and S.Yan)

[20] A Neumann problem in exterior domain, Manuscripta Mathematica, 106(2001), 63-74.(with M. Lucia and H.S. Zhou)

[21] On the scalar curvature equation -∆u=(1+εK)u(N+2)/(N-2) in RN, Calc. Var. and PDE, 15(2002), 403-419. (with E.S.Noussair and S.Yan)

[22] Uniqueness of positive multi-lump bound states of nonlinear

Schrodinger equations, Math. Zeit., 243(2003), 599-642.(with H.P. Heinz)

[23] A compactness result for singular elliptic problems involving

critical Sobolev exponent, Proc. Amer.Math. Soc.,131(2003), 1857 - 1866. (with S.Peng)

[24] Solutions for semilinear elliptic equations with critical exponents and Hardy potential, J. Diff. Equat., 205(2004), 521-537.(with P.Han)

[25] Multi-bump standing waves with a critical frequency for nonlinear Schrodinger equations, J. Diff. Equat., 203(2004), 292-312.(with E. S. Noussair)

[26] High energy positive solutions for Neumann problem for an elliptic system of equations with critical nonlinearity, Calc. Var. and PDE, 25(2005), 161-185. (with P. Han)

[27] Asymptotic behavior for elliptic problems with singular coefficient and nearly critical Sobolev growth, Annali di Mat. Pura ed Appl., 185 (2006), 189-205. (with S.Peng)

[28] Multi-bump bound states of Schrodinger equations with a critical frequency, Math. Ann., 336(2006), 925-948.(with S.Peng)

[29] Effective macroscopic dynamics of stochastic partial differential equations in perforated domains, SIAM J.Math.Anal., 38 (2007), 1508 -1527. (with J. Duan and W.Wang)

[30] Multiscale-bump standing waves with a critical frequency for nonlinear Schrodinger equations, Trans. Amer. Math. Soc.,360 (2008), 3813 - 3837. (with E.S.Noussair and S.Yan)

[31] Semi-classical bound states for Schrodinger equations with potentials vanishing or unbounded at infinity, Comm. Part. Diff. Equat., 34 (2009), 1566--1591. (with S.Peng)

[32] Infinitely many solutions for an elliptic problem involving

critical Sobolev growth and Hardy potential, Calc.Var. and PDE., 38(2010), 471-501.(with S.Yan)

[33] Multiplicity of solutions for the plasma problem in two dimensions, Adv. Math., 225 (2010), 2741-2785.(with S.Peng and S.Yan)

[34] Local exact controllability of the Navier-Stokes equations with

the condition on the pressure on parts of the boundary, SIAM J. Control Optim., 48(2010), 3805-3837.(with T.Kim)

[35] Divergent solutions to the 5D Hartree equations,Colloq. Math., 125 (2011), 255-287.(with Q.Guo)

[36] Infinitely many solutions for p-Laplacian equation involving critical Sobolev growth, J. Funct. Anal., 262 (2012), 2861-2902.(with S.Peng and S.Yan)

[37] Continuous dependence of Cauchy problem for nonlinear Schrodinger equation in H^s, J. Diff. Equat., 255 (2013),2018-2064.(with W.Dai and W.Yang)

[38] Concentration of solutions for the Yamabe problem on half -spaces. Proc. Roy. Soc. Edinburgh, Sect. A 143 (2013),no. 1, 73-99.(with S.Peng)

[39] On the Webster scalar curvature problem on the CR sphere with a

cylindrical- type symmetry, J. Geom. Anal., 23(2013),1674-1702.

(with S. Peng and S.Yan)

[40] Minimal blow-up solutions of mass-critical inhomogeneous Hartree equation. J. Math. Phys., 54 (2013), no. 12, 121511, 25 pp. (with Su Yiming)

[41] Regularization of point vortices pairs for the Euler equation in dimension two. Arch. Ration. Mech. Anal., 212 (2014), no. 1, 179–217. (with Liu Zhongyuan and Wei Juncheng)

[42] Uniqueness of positive bound states with multi-bump for nonlinear Schrödinger equations. Calc. Var. Partial Differential Equations, 54 (2015), no. 4, 4037–4063. (with Li Shuanglong and Luo Peng)

[43] Dynamics for a stochastic reaction-diffusion equation with additive noise. J. Differential Equations, 259 (2015), no. 3, 838–872. (with Sun Chunyou and Yang Meihua)

[44] Planar vortex patch problem in incompressible steady flow. Adv. Math., 270 (2015), 263–301. (with Peng Shuangjie and Yan Shusen)

[45] Non-stationary Navier-Stokes Equations with Mixed Boundary Conditions, J. Math. Sci. Univ. Tokyo, 24 (2017), 159–194.(with Tujin Kim)

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