个人资料

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姓 名：徐润章


职 称：教授
电 话：**
传 真：
邮 箱：xurunzh@163.com
个人简介


哈尔滨工程大学-理学院-数学研究中心-教授，博士，硕士生导师，博士生导师。美国数学会(AMS)会员；美国数学评论(MR)评论员；黑龙江省数学会常务理事；国际数学物理联合会会员；中国科技论文在线特聘评审专家，《数学研究期刊》编委。

近年来一直从事非线性发展方程定解问题的动力学形态研究,特别是在位势井理论框架下针对非线性偏微分方程的解在不同初始能量状态下的适定性进行研究.通过构建所研究问题的能量泛函、势能泛函与Nahari泛函,分析初值与整体解存在性之间的关系,给出整体解存在与非存在的门槛条件.特别是针对超临界能量情形推导出若初值属于新的稳定集合整体解存在,若初值位于新的不稳定集合内整体解非存在.



先后在国内外学术刊物上发表有关学术论文50余篇,其中具代表性的成果是在位势井结构框架内针对具强耗散的半线性伪拟抛物方程的初边值问题就初始能级的不同状态下的整体解适定性进行了全面且系统的理论分析,结合极大值原理与比较原理在强阻尼存在的情形下得到了保证半线性伪拟抛物方程的高能整体解存在与非存在的充分条件.此成果发表于本领域重要刊物《Journal of Functional Analysis》；通过引入一族位势井结合Galerkin方法与凹函数方法证明了具复杂高阶非线性应力项与线性弱耗散项的非线性波动方程整体解的存在性与非存在性,得到了低临界与临界能量状态下相应的门槛条件,此成果发表于本领域重要刊物《Journal of Differential Equations》; 利用极值原理给出了具多个正项吸收源的非线性抛物方程的有限时间淬火现象, 结合有界性分析估计出了淬火时间的上下界, 发现问题出现淬火的次数与吸收源的个数有关,揭示出了复杂非线性项的结构对淬火问题产生的影响,此成果发表于本领域重要刊物《Nonlinear Analysis Series B: Real World Applications》.发表论文被引频次总计80次,他引频次达40余次,平均引用次数1.95,并3次被列为相关刊物的Top25列表.近5年发表录用论文42篇,其中被SCI收录35篇.

研究方向：非线性发展方程，系统理论，非线性动力系统。



招生专业：硕士：应用数学（招生院系 理学院）

博士：控制科学与工程（招生院系 自动化学院）

http://heuac.hrbeu.edu.cn/zidonghuaxueyuan/ShowArticle.asp?ArticleID=144486

博士后流动站：控制科学与工程（招生院系 自动化学院）

科研项目：主持，参与，完成4项国家自然科学基金项目（#**主要成员，#**主要成员, #**主持，#**主持,# **主持）；主持1项博士点基金项目；1项博士后基金一等资助；2项中央高校基础科研业务费资助项;2项哈尔滨工程大学基础研究基金项目；1项哈尔滨工程大学培育基金项目（HEUFP05032），2项黑龙江省自然科学基金项目（A2007-02主要成员；A2008-10主要成员）；一项哈尔滨工程大学2005年度创新项目；1项2009年度黑龙江省教育厅科学技术研究面上项目（**主要成员)。

科研著作：近5年在核心刊物发表录用论文75篇，其中被EI收录26篇，被SCI收录36篇，主编教材1部，在国外合作出版专著1部，参编教材2部。其中在著名SCI刊物Journal of Differential Equations, Journal of Functional Analysis, Physica D: Nonlinear Phenomenon, Journal of Mathematical Physics, Nonlinear Analysis: Theory, Methods & Applications, Journal of Mathematical Analysis and Applications, Communications on Pure and Applied Analysis, Applied Mathematics and Mechanics, Discrete and Continuous Dynamical System-Series , Zeitschrift für Angewandte Mathematik und Physik发表的论文被引用60余次，并3次被列为相关刊物的Top25列表。

业绩成果


担任教学工作：

本科：数学物理方程； 概率论与数理统计； 专业英语

研究生：系统科学概论； 非线性动力系统； 偏微分方程中的泛函分析方法； 非线性发展方程



近期发表论文部分列表：

[1] Xu Runzhang, Su Jia, Global existence and finite time blow-up for a class of semilinear pseudo-parabolic equations, Journal Functional Analysis, 2013, 264: 2732-2763.

[2] Xu Runzhang, Xu Chuang. Sharp conditions of global existence for second-order derivative nonlinear Schrodinger equations with combined power-type nonlinearities, ZAMM- Z. Angew. Math. Mech, 2013,93(1):29-37.

[3] Xu Runzhang, Liu Jie, Niu Yi, Chen Shaohua, Asymptotic behaviour of solution for multidimensional viscoelasticity equation with nonlinear source term, Boundary Value Problems 2013, 2013:42 .

[4] Shen Jihong, Yang Yanbing, Chen Shaohua, Xu Runzhang. Finite time blow up of fourth order wave equations with nonlinear strain and source terms at high energy level, International Journal of Mathematics, 24(5)(2013)**-1-8.

[5] Xu Runzhang, Ding Yunhua. Global solutions and finite time blow up for damped Klein-Gordon equation, Acta Matematica Scientia, 2013,33B(3):643-652.

[6] Xu Runzhang, Yang Yanbing, Global existence and asymptotic behaviour of solutions for a class of fourth order strongly damped nonlinear wave equations, Quarterly of Applied Mathematics, 2013,52(3):401-415.

[7] Xu Runzhang, Wang Shuo, Yang Yanbing, Ding Yunhua, Initial boundary value problem for a class of fourth order wave equation with viscous damping term, Applicable Analysis: An International Journal, 2013,92(7):1403-1416.

[8] Xu Runzhang, Yang Yanbing, Chen Shaohua, Su Jia, Shen Jihong, Huang Shaobin, Nonlinear wave equations and reaction-diffusion equations with several nonlinear source terms of different signs at high energy level, Australian and New Zealand Industrial and Applied Mathematics Journal- ANZIAM Journal, 2013， 54;153-170.

[9] Xu Runzhang, Xu Chuang, Cross-constrained problems for nonlinear Schrodinger equation with harmonic potential，Electronic Journal of Differential Equations，2012,2012(211):1-12.

[10] Xu Runzhang, Jiang Xiaoli, Liu Jie, Uniform blow-up rate for a compressible reactive gas model, Applied Mathematics and Mechanics(English Edition), 2012,33(1):129-138.

[11] Xu Runzhang, Cao Xiuying, Yu Tao, Finite time blow-up and global solutions for a class of semilinear parabolic equations at high energy level, Nonlinear Analysis Series B: Real World Applications,2012, 13(1)197-202.

[12] Xu Runzhang, Jin Chunyan, Yu Tao, Liu Yacheng, On quenching for some parabolic problems with combined power-type nonlinearities, Nonlinear Analysis Series B: Real World Applications, 13(2012)333-339.

[13] Xu Runzhang, Liu Yacheng, Ill-posedness of nonlinear parabolic equation with critical initial condition, Mathematics and Computers in Simulation 82(2012) 1363-1374.

[14] Xu Runzhang, Yang Yanbing, Finite time blow up for the nonlinear fourth-order dispersive-dissipative wave equation at high energy level, International Journal of Mathematics, 23(5)(2012)**-1-10.

[15] Jiang Xiaoli, Xu Runzhang, Global well-posedness for semilinear hyperbolic equations with dissipative term, Journal of Applied Mathematics and Computing, 2012,38(1-2):467-487.

[16] Jiang Xiaoli, Yang Yanbing, Xu Runzhang, Family potential wells and its applications to NLS with harmonic potential, Applied Mathematics & Information Sciences, 6(1S)(2012) 155S-165S.

[17] Xu Runzhang, Xu Chuang, Liu Yang, Yu Tao. Well-posedness of nonlinear wave equation with combined power-type nonlinearities, Mathematical Methods in the Applied Sciences, 2011,34(8)869-895.

[18] Xu Runzhang, Liu Yacheng, Liu Bowei. The Cauchy problem for a class of multidimensional Boussinesq type equation, Nonlinear Analysis: Theory, Methods & Applications,2011,74(6)2425-2437.

[19] Xu Runzhang, Cauchy problem of generalized Boussinesq equation with combined power-type nonlinearities, Mathematical Methods in the Applied Sciences, 2011,34(18)2318-2328

[20] Xu Runzhang. Global existence, blow up and asymptotic behaviour of solutions for nonlinear Klein-Gordon equation with dissipative term, Mathematical Methods in Applied Science, 2010, 33, 831–844.

[21] Xu Runzhang, Initial boundary value problem of semilinear hyperbolic equations and parabolic equations with critical initial data, Quarterly of Applied Mathematics,2010，LXVIII（3）：459–468.

[22] Xu Runzhang，Xu Chuang. Nonlinear Schrodinger equation with combined power-type nonlinearities and harmonic potential, Applied Mathematics and Mechanics(English Edition), 31(4), 521-528 (2010)

[23] Xu Runzhang, Liu Yacheng, Global existence and blow-up of solutions for generalized Pochhammer-Chree equations, Acta Mathematica Scientia, 2010,30B(5):1793–1807

[24] Xu Runzhang, Yu Tao. Remarks on wave equations involving two opposite nonlinear source terms. Journal of Applied Mathematics and Computing, 2009，29（1-2）：15-18.

[25] Xu Runzhang, Liu Yang, Wu Weining. The depth of potential wells and their computations, The Sixth IMACS International Conference on Nonlinear Evolution Equations and Wave Phenomena: Computation and Theory. Georgia, USA. March 23-26, 2009.

[26] Liu Yacheng, Xu Runzhang. Generalized Boussinesq equations with various power type nonlinearities. The Sixth IMACS International Conference on Nonlinear Evolution Equations and Wave Phenomena: Computation and Theory. Georgia, USA. March 23-26, 2009.

[27] Liu Yacheng, Xu Runzhang. Local well posedness of Cauchy problem for viscous diffusion equations，International Journal of Mathematics, 2009,20(4):509-519.

[28] Runzhang Xu, Yacheng Liu, Global existence and nonexistence of solution for Cauchy problem of multidimensional double dispersion equations, Journal of Mathematical Analysis and Applications, 2009,359(2): 739-751.

[29] Runzhang Xu, Yacheng Liu, Tao Yu, Global existence of solution for Cauchy problem of multidimensional generalized double dispersion equations, Nonlinear Analysis: Theory, Methods & Applications, 2009,71(10) :4977-4983.

[30] Liu Yacheng, Xu Runzhang. Family of potential wells and its applications to Boussinesq equations. XVI International Congress on Mathematical Physics, Prague, August 3-8, 2009.

[31] Xu Runzhang, Wu Weining. Varitional method to evolution equation with combined power-type. XVI International Congress on Mathematical Physics, Prague, August 3-8, 2009.

[32] Yu Tao, Tang Liqiang, Xu Runzhang. Qualitative analysis of a nonlinear viscous diffusion equation, Nonlinear Analysis: Theory, Methods & Applications,2009，71：1059-1064.

[33] Xu Runzhang, Shen Jihong. Some generalized results for global well-poseness for wave equations with damping and source terms, Mathematics and Computers in Simulation, 80(2009):804-807.

[34] Xu Runzhang. Asymptotic behavior and blow up of solutions for semilinear parabolic equations at critical energy level, Mathematics and Computers in Simulation, 80(2009):808-813.

[35] Liu Yacheng, Xu Runzhang. Potential well method for Cauchy problem of generalized double dispersion equations, Journal of Mathematical Analysis and Applications, 338 (2008) 1169–1187.

[36] Liu Yacheng, Xu Runzhang. A class of fourth order wave equations with dissipative and nonlinear strain terms, Journal of Differential Equations, 244 (2008) 200–228.

[37] Xu Runzhang, Zhao Xiren, Shen Jihong. Asymptotic behavior of solutions for the fourth order wave equation with dispersive and dissipative terms[J]. Applied Mathematics and Mechanics(English Edition), 2008，29(2)：259-262.

[38] Liu Yacheng, Xu Runzhang. Potential well method for initial boundary value problem of the generalized double dispersion equations, Communications on Pure and Applied Analysis, 7 (2008), no. 1, 63-81. 2008.1

[39] Liu Yacheng, Xu Runzhang，Yu Tao. Global existence, nonexistence and asymptotic behavior of solutions for Cauchy problem of semilinear heat equations, Nonlinear Analysis-Theory Methods & Applications，2008，68(11)：3332-3348. 2008.6.11

[40] Xu Runzhang, Liu Yacheng. Remarks on nonlinear Schr?dinger equation with harmonic potential. Journal of Mathematical Physics, 2008, 49(4),: 043512-043512-5.
R. Xu,Y. Liu. Remarks on nonlinear Schr?dinger equation with harmonic potential. J. Math. Phys. 49, 043512 (2008) 2008-4

[41] Liu Yacheng, Xu Runzhang. Global existence and blow up of solutions for Cauchy problem of generalized Boussinesq equation, Physica D: Nonlinear Phenomena, 2008，237：721–731.

[42] Xu Runzhang, Liu Yacheng. Asymptotic behavior of solutions for initial boundary value problem of strongly damped nonlinear wave equations[J]. Nonlinear Analysis Series A: Theory, Methods & Applications, 2008, 69(8): 2492-2495. 2008-10-15

[43] Xu Runzhang, Zhang Wenying, Wu Weining. Wave equations and reaction-diffusion equations with two nonlinear source terms of different sign[M]. Invited Article, Nonlinear Analysis Research Trends, Inès N. Roux (Editor-in-Chief), Hauppauge: Nova Science Publishers, pp 259-281, 2008, 2nd Quarter, ISBN: 978-1-60456-358-0

[44] Wu Weining ,Xu Runzhang, Zhang Wenying,. Global Well-posedness of a Class of Nonlinear Wave Equations and Heat Equations, International Journal of Evolution Equations, Volume 4 Issue 3, pp. 321-344（2008）

[45] XU Runzhang. Asymptotic behavior and blow up of solutions for the viscous diffusion equation, Applied Mathematical Letters.20 (2007) 255-259.

[46] Liu Yacheng, Xu Runzhang, Fourth order wave equations with nonlinear strain and source terms, Journal of Mathematical Analysis and Applications,331 (2007) 585–607.

[47] Liu Yacheng, Xu Runzhang. Wave equations and reaction-diffusion equations with several nonlinear source terms of different sign，Discrete and Continuous Dynamical System-Series B,2007,7(1):171-189.



科研项目列表：

2005.1-2007.12 黑龙江省教育厅科研项目

2005.1-2006.12 哈尔滨工程大学基础研究基金项目

2007.12-2009.12 黑龙江省自然科学基金项目

2009.1-2011.1 哈尔滨工程大学基础研究基金项目（引进人才）

2009.1-2010.12 黑龙江省自然科学基金项目

2009.1-2011.12 国家自然科学基金

2009.1-2010.12 黑龙江省教育厅科学技术研究面上项目

2010.1-2010.12 国家自然科学基金

2010.1-2010.12 中央高校基本科研业务费专项资金自由探索计划

2011.1-2012.1 高等学校博士学科点专项科研基金

2012.1-2014.12 国家自然科学基金

2012.1-2013.6 黑龙江省教育厅科学技术研究项目

2015.1-2018.12 国家自然科学基金

科研获奖：

2009.6.17 第11届黑龙江省自然科学技术学术成果二等奖

2010.10 哈尔滨市自然科学技术学术成果二等奖

2010.4.9 黑龙江省高校科学技术一等奖

2010.9 黑龙江省科学技术三等奖



学术活动与学术组织任职：

l 2007年4月16日到4月19日参加在美国乔治亚州乔治亚大学召开的The Fifth IMACS International Conference on Nonlinear Evolution Equations and Wave Phenomena: Computation and Theory.作专题报告30分钟，发表会议论文2篇。

l 2007年12月17日到22日参加在杭州召开的“The Fourth International Congress of Chinese Mathematicians”（第四届华人数学家大会，做分会报告，发表会议论文3篇）。

l 如下刊物的审稿人：Nonlinear Analysis, Applied Mathematical Letters, Journal of Mathematical Analysis and Application, Acta Mathematica Sinica，Acta Mathematicae Applicatae Sinic，Applied Mathematics and Mechanics, Journal of Partial Differential Equations, Applications and Applied Mathematics, Scientific Research and Essays，Journal of Mechanical Engineering Research，数学学报，应用数学学报，数学进展，大学数学，兰州大学学报，上海交通大学学报。

l 2009年应邀担任The Sixth IMACS International Conference on Nonlinear Evolution Equations and Wave Phenomena: Computation and Theory分会主席.

l 2012 应邀参加International Conference on Nonlinear Evolutionary Partial Differential Equation- Theories and Applications并做大会报告。

l 2013年应邀担任The Sixth IMACS International Conference on Nonlinear Evolution Equations and Wave Phenomena: Computation and Theory分会主席并做分组报告.

l 2013年应邀参加2013 CMS (The Canadian Mathematical Society) Summer Meeting并做分组报告。

l 2013年应邀参加The Sixth International Congress of Chinese Mathematicians并做分组报告.

l 2014年应邀参加The 10th AIMS conference on Dynamical Systems, Differential Equations and Applications并做分组报告.

l 2014年应邀参加International Congress of Mathematicians 2014并做分组报告.