崔尚斌

崔尚斌

教育背景:19789月至19886月在兰州大学数学力学系历读本科生、硕士研究生和博士研究生。19886月获理学博士学位。

工作经历 19859月至199910月在兰州大学数学力学系历任助教、讲师、副教授和教授,其中于19909月任副教授和硕士研究生导师,19929月破格任教授,19959月起任博士研究生导师。199910月至今在中山大学数计学院工作,任教授和博士生导师。

访学经历:分别于19983月至19992月在美国明尼苏达大学数学及其应用研究所、200110月至20029月在美国俄亥俄州立大学数学系、20089月至20098月在美国芝加哥大学数学系做访问学者,并曾于2005年夏和2007年夏分别在德国汉诺威大学应用数学研究所和法国巴黎高等师范学校数学及其应用系各访问两个月和三个月。

 

 

电话:020-84110137

职称:教授

邮箱:cuishb@mail.sysu.edu.cn

 


研究成果:

研究成果1

主要科研项目:

1)应用偏微分方程的若干问题, 国家自然科学基金面上项目,20161月至201912月。

2)生物学和物理学中的偏微分方程问题,国家自然科学基金面上项目,20121月至 201512月。

3)肿瘤生长的自由边界问题和非线性发展方程,国家自然科学基金面上项目,20081月至201012月。

4)非球对称肿瘤生长的自由边界问题,国家自然科学基金面上项目,20051月至200712月。

5)肿瘤生长的自由边界问题,国家自然科学基金面上项目,20021月至200412月。

著作:

1) 《偏微分方程现代理论》,科学出版社,2016.

2) 《数学分析教程(上、中、下)》,科学出版社,2013.

3) 《幂零Lie群上的Fourier分析和不变偏微分算子》,兰州大学出版社,1993.

4) 《解析几何》,兰州大学出版社,1993.

论文:

  迄今已独立或与合作者合作发表论文160余篇。以下是近十年来独立或为第一作者发表的研究论文:

[1] (with Meng Bai) Mathematical analysis of population migration and itseffects to spread of epidemics, Discrete andContinuous Dynamical Systems Series B, 29(2015), no.9, 2819-2858.

[2] Linearized stability for a multi-dimensional free boundary problem modelling two-phase tumour growth,Nonlinearity, 27(2014), no.2, 1--35.

[3] Asymptotic stability of the stationarysolution for a parabolic hyperbolic free boundary problem modeling tumor growth,SIAM Journal of Mathematical Analysis, 45(2013), no.5,2870–2893.

[4] (with Carlos E. Kenig) Weak continuity of the flow map for theBenjamin-Ono equation on the line, Journal of Fourier Analysis andApplications, vol.16 (2010), no. 6, pp.1021-1052.

[5] (with Carlos E. Kenig) Weak continuity of dynamical systems for the KdVand mKdV equations. Differential and Integral Equations, vol.23 (2010), no.11-12, pp.1001-1022.

[6] Lie group action and stability analysis of stationary solutions for afree boundary problem modelling tumor growth. Journal of DifferentialEquations, 246(2009), no.5, 1845--1882.

[7] (with Joachim Escher) Well-posedness and stability of a multidimensionaltumor growth model,Archive for Rational Mechanics and Analysis,191(2009), no.1,173--193.

[8] Asymptotic stability of the stationary solution for a hyperbolic free boundary problem modeling tumor growth, SIAM Journal of MathematicalAnalysis, 41(2008), no.4, 1692--1724.

[9] (with Joachim Escher) Asymptotic behavior of solutions of amultidimensional moving boundary problem modeling tumor growth,  Communications on Partial DifferentialEquations, 33(2008), no.4--6, 636--655.

[10] Well-posedness of a multidimensional free boundary problem modeling thegrowth of nonnecrotic tumors, Journal of Functional Analysis, 245(2007), no.1,1--18.

[11] (with Joachim Escher) Bifurcation analysis of an elliptic free  boundary problem modeling growth of avasculartumors, SIAM Journal  of MathematicalAnalysis, 39(2007), no.1, 210--235.

[12] (with Shihe Xu) Analysis of mathematical models for the growth of  tumors with time delays in cellproliferation, Journal of Mathematical Analysis and Applications, 336(2007),no. 1, 523--541.

[13] (with Cuihua Guo) Well-posedness of higher-order nonlinear Schrodingerequations in Sobolev spaces Hs(Rn) and applications, Nonlinear Analysis, Theory, Methods and Applications,67(2007), no.3, 687--707.

[14]  Pointwise estimates foroscillatory integrals and related Lp-Lq estimates II: multidimensional case, Journal of Fourier Analysisand  Applications, 16(2006), no.6,605--627.

[15] Existence of a stationary solution for the modified Ward-King  tumor growth model, Advances in AppliedMathematics, 36(2006), no.4, 421--445.

[16] Formation of necrotic cores in the growth of tumors: analytic  results, Acta Mathematica Scientia (EnglishSeries), 26(2006), no.4, 781--796.

[17] (with Donggao Deng and Shuangping Tao) Global existence of solutionsfor the Cauchy problem of the Kawahara equation with L2  initial data, Acta Mathematica Sinica(English Series), 22(2006), no.5,1457--1466.