李玉祥（东南大学博士生导师）

人物经历

现任东南大学教授、博士、博士生导师。

2004.12-至今，东南大学数学学院。

2008.2-2009.2，法国巴黎十三大数学系访问学者。

2002.12-2004.12，南京大学地球科学系博士后。^[1]

主要成就

研究方向

非线性偏微分方程理论及其应用；非线性Keller-Segel方程的长时间渐近行为、爆破性态分析；非线性热方程的的长时间渐近行为、爆破性态分析；KPZ界面方程的长时间渐近行为、梯度爆破性态分析。

文章目录

1. Li, Feng; Li, Yuxiang Global existence and boundedness of weak solutions to a chemotaxis-Stokes system with rotational flux term. Z. Angew. Math. Phys. 70 (2019), no. 4, Art. 102, 21 pp.
2. Wang, Hengling; Li, Yuxiang Renormalized solutions to a chemotaxis system with consumption of chemoattractant. Electron. J. Differential Equations 2019, Paper No. 38, 19 pp.
3. Wang, Hengling; Li, Yuxiang On a parabolic-parabolic system with gradient dependent chemotactic coefficient and consumption. J. Math. Phys. 60 (2019), no. 1, 011502, 20 pp.
4. Tao, Weirun; Li, Yuxiang Global weak solutions for the three-dimensional chemotaxis-Navier–Stokes system with slow p-Laplacian diffusion. Nonlinear Anal. Real World Appl. 45 (2019), 26–52.
5. Yan, Jianlu; Li, Yuxiang Global generalized solutions to a Keller-Segel system with nonlinear diffusion and singular sensitivity. Nonlinear Anal. 176 (2018), 288–302.
6. Zhang, Qingshan; Li, Yuxiang Global solutions in a high-dimensional two-species chemotaxis model with Lotka-Volterra competitive kinetics. J. Math. Anal. Appl. 467 (2018), no. 1, 751–767.
7. Li, Yan; Li, Yuxiang; Global boundedness of solutions for the chemotaxis-Navier–Stokes system in R.

   J. Differential Equations

   261 (2016), no. 11, 6570–6613.
8. Zhang, Qingshan; Li, Yuxiang An attraction-repulsion chemotaxis system with logistic source. ZAMM

   Z. Angew. Math. Mech.

    96 (2016), no. 5, 570–584.^[1]
9. Li, Yan; Li, Yuxiang Blow-up of nonradial solutions to attraction–repulsion chemotaxis system in two dimensions.

   Nonlinear Anal. Real World Appl.

    30 (2016), 170–183.
10. Zhang, Qingshan; Li, Yuxiang Boundedness in a quasilinear fully parabolic Keller-Segel system with logistic source.

    Z. Angew. Math. Phys.

     66 (2015), no. 5, 2473–2484.
11. Zhang, Qingshan; Li, Yuxiang Convergence rates of solutions for a two-dimensional chemotaxis-Navier-Stokes system.

    Discrete Contin. Dyn. Syst. Ser.

     B 20 (2015), no. 8, 2751–2759.
12. Zhang, Qingshan; Li, Yuxiang Stabilization and convergence rate in a chemotaxis system with consumption of chemoattractant.

    J. Math. Phys.

     56 (2015), no. 8, 081506, 10 pp.
13. Zhang, Qingshan; Li, Yuxiang Global weak solutions for the three-dimensional chemotaxis-Navier-Stokes system with nonlinear diffusion.

    J. Differential Equations

    259 (2015), no. 8, 3730–3754.
14. Wang, Wenjia; Li, Yuxiang Stabilization in an n-species chemotaxis system with a logistic source.

    J. Math. Anal. Appl.

     432 (2015), no. 1, 274–288.
15. Zhang, Qingshan; Li, Yuxiang Global boundedness of solutions to a two-species chemotaxis system.

    Z. Angew. Math. Phys.

     66 (2015), no. 1, 83–93.
16. Li, Yan; Li, Yuxiang Finite-time blow-up in higher dimensional fully-parabolic chemotaxis system for two species.

    Nonlinear Anal.

     109 (2014), 72–84.
17. Zhang, Qingshan; Li, Yuxiang Global existence and asymptotic properties of the solution to a two-species chemotaxis system.

    J. Math. Anal. Appl.

    418 (2014), no. 1, 47–63.
18. Liu, Xiaopan; Li, Yuxiang On the stability of global solutions to the 3D Boussinesq system.

    Nonlinear Anal.

     95 (2014), 580–591.
19. Liang, Fei; Liu, Qi Lin; Li, Yu Xiang On a nonlocal problem modelling Ohmic heating in planar domains.

    Acta Math. Sin.

     (Engl. Ser.) 29 (2013), no. 3, 523–534.
20. Li, Yuxiang; Wen, Xuefei Existence of multi-bump solutions for coupled Schrödinger systems.

    J. Southeast Univ.

     (English Ed.) 28 (2012), no. 4, 496–501.
21. Li, Yuxiang Optimal conditions for a priori estimates for semilinear elliptic systems with two components.

    Nonlinear Anal.

     72 (2010), no. 3-4, 1850–1864.^[1]
22. Li, Yuxiang; Souplet, Philippe Single-point gradient blow-up on the boundary for diffusive Hamilton-Jacobi equations in planar domains.

    Comm. Math. Phys.

     293 (2010), no. 2, 499–517.
23. Li, Yuxiang Stabilization towards the steady state for a viscous Hamilton-Jacobi equation.

    Commun. Pure Appl. Anal.

     8 (2009), no. 6, 1917–1924.
24. Fei, Liang; Yuxiang, Li Blow-up for a nonlocal parabolic equation.

    Nonlinear Anal.

    71 (2009), no. 7-8, 3551–3562.
25. Qilin, Liu; Fei, Liang; Li, Yuxiang Asymptotic behaviour for a non-local parabolic problem.

    European J. Appl. Math.

     20 (2009), no. 3, 247–267.
26. Li, Yuxiang Optimal conditions for L-regularity and a priori estimates for semilinear elliptic systems.

    J. Math. Anal. Appl.

     351 (2009), no. 1, 257–276.
27. Wang, Xianchao; Li, Yuxiang Asymptotical behavior of a nonlocal hyperbolic problem.

    Far East J. Dyn. Syst.

    10 (2008), no. 2, 153–167.
28. Liu, Qilin; Li, Yuxiang; Gao, Hongjun Uniform blow-up rate for diffusion equations with nonlocal nonlinear source.

    Nonlinear Anal.

     67 (2007), no. 6, 1947–1957.
29. Liu, Qilin; Li, Yuxiang; Gao, Hongjun Uniform blow-up rate for a nonlocal degenerate parabolic equations.

    Nonlinear Anal.

     66 (2007), no. 4, 881–889.
30. Liu, Qi Lin; Li, Yu Xiang; Gao, Hong Jun Blow-up property for a reaction-diffusion system with nonlocal sources. (Chinese)

    Acta Math. Sinica

    (Chin. Ser.) 49 (2006), no. 4, 869–882.
31. Liu, Qilin; Li, Yuxiang; Gao, Hongjun Uniform blow-up rate for diffusion equations with localized nonlinear source.

    J. Math. Anal. Appl.

     320 (2006), no. 2, 771–778.
32. Zou, Xiao Rong; Li, Yao Wen; Li, Yu Xiang The first eigenvalue λ1, p of the p-Laplace operator.

    Nihonkai Math. J.

     16 (2005), no. 2, 129–133.
33. Li, Yuxiang; Wu, Jichun Extinction for fast diffusion equations with nonlinear sources.

    Electron. J. Differential Equations

    2005, no. 23, 7 pp. (electronic).
34. Li, Yuxiang; Xie, Chunhong Blow-up for semilinear parabolic equations with nonlinear memory.

    Z. Angew. Math. Phys.

     55 (2004), no. 1, 15–27.^[1]
35. Deng, Weibing; Li, Yuxiang; Xie, Chunhong A nonlinear degenerate parabolic system with non-local source and crosswise-diffusion.

    Z. Angew. Math. Phys.

     54 (2003), no. 3, 503–516.
36. Liu, Qi Lin; Li, Yu Xiang; Xie, Chun Hong Blow-up of solutions to a degenerate parabolic equation with localized nonlinear reactions. (Chinese)

    Acta Math. Sinica

    (Chin. Ser.) 46 (2003), no. 6, 1135–1142.
37. Li, Yuxiang; Xie, Chunhong Quasilinear parabolic systems of several components.

    Math. Ann.

     327 (2003), no. 2, 395–407.
38. Deng, Weibing; Yuxiang, Li; Chunhong, Xie Global existence and nonexistence for a class of degenerate parabolic systems.

    Nonlinear Anal.

     55 (2003), no. 3, 233–244.
39. Deng, Weibing; Li, Yuxiang; Xie, Chunhong Semilinear reaction-diffusion systems with nonlocal sources.

    Math. Comput. Modelling

    37 (2003), no. 9-10, 937–943.
40. Deng, Weibing; Li, Yuxiang; Xie, Chunhong Existence and nonexistence of global solutions of some nonlocal degenerate parabolic equations.

    Appl. Math. Lett.

     16 (2003), no. 5, 803–808.
41. Li, Yuxiang; Xie, Chunhong Blow-up for p-Laplacian parabolic equations.

    Electron. J. Differential Equations

     2003, No. 20, 12 pp.
42. Deng, Weibing; Li, Yuxiang; Xie, Chunhong Blow-up and global existence for a nonlocal degenerate parabolic system.

    J. Math. Anal. Appl.

     277 (2003), no. 1, 199–217.
43. Li, Yuxiang; Liu, Qilin; Xie, Chunhong Semilinear reaction-diffusion systems of several components.

    J. Differential Equations

    187 (2003), no. 2, 510–519.^[1]
44. Deng, Weibing; Li, Yuxiang; Xie, Chunhong Existence and nonexistence of global solutions of some non-local degenerate parabolic systems.

    Proc. Amer. Math. Soc.

     131 (2003), no. 5, 1573–1582.
45. Li, Yuxiang; Deng, Weibing; Xie, Chunhong Global existence and nonexistence from degenerate parabolic systems.

    Proc. Amer. Math. Soc.

     130 (2002), no. 12, 3661–3670.

主持项目

国家自然科学基金，11671079，非线性Keller-Segel方程的定性研究，2017.01-2020.12。

国家自然科学基金，11171063，带非线性梯度项的抛物型方程的定性研究，2012.01-2015.12。

江苏省自然科学基金，BK2010404，KPZ方程解的渐近性质，2010.08-2013.08。

国家自然科学基金，10601012，非线性抛物型方程的blow-up现象，2007.01-2009.12。

参加会议

2016.10.14-16，2016可积系统与偏微分方程国际学术研讨会，江苏大学，镇江。

2016.09.22-25，“反应扩散方程及其应用”学术研讨会，江苏师范大学，徐州。^[1]

2016.07.01-05，The 11th AIMS Conference on Dynamical Systems, Differential Equations and Applications，Orlando, Florida，USA.

2015.12.25-27，长江三角洲偏微分方程学术研讨会，复旦大学。

2015.8.19-22，高校数学类专业涉及“教材建设”和“课堂讲授”的教学研讨会，兰州大学。

2015.8.7-9，非线性偏微分方程及其应用国际学术会议，北京工业大学。

2015.8.1-3，第十三届非线性偏微分方程暑期讲习班国际学术会议，华中师范大学。

2015.5.21-24，Recent advances in reaction-diffusion equations and applications，江苏师范大学。

2014.12.5，非线性偏微分方程青年论坛，南京航空航天大学。

2014.8.1-5，第十二届非线性偏微分方程暑期讲习班国际学术会议，四川师范大学。

2014.6.27-28，“应用偏微分方程及其数值计算”青年论坛流体与生物中的偏微分方程专题。^[1]

2013.12.21-22,长江三角洲偏微分方程学术研讨会暨博士生论坛，同济大学。

2013.8.1-4,第十一届非线性偏微分方程暑假讲习班和学术研讨会，北京工业大学。

2012.9.10-14, 5th Euro-Japanese Workshop on Blow-Up, Marseille, France.

2012.5.21-25, 7th European Conference on Elliptic and Parabolic Problems, Gaeta, Italy.

所带学生

博士后：李彬（2020.01）硕士生：金泰安、毛亚茹（2020），余丽伶（2019），毛宣、孙春雷（2018），刘萌（2017），张伟洪（2016），杨盼（2013），刘姣、郭楠楠（2012），冯燕、温雪飞、马园园（2009），胡艾香（2008），秦明方、梁金雨（2007），汪先超、梁飞（2006）。

博士生：谢周猛（2020.3），刘萌（硕转博2019.9），王万万（2018.3），王恒玲（2017.9），李锋（2016.3），闫建璐（本科直博2015.9），陶为润（本科直博2014.9），张清山（2013.3），李燕（硕博连读 2011.9），刘晓盼（2011.9），王文佳（硕博连读2010.9）^[1]

★闫建璐2019.10-2020.10赴德国联合培养。

★陶为润2018.10-2019.10赴德国联合培养。

★李燕2014.9-2015.9赴德国联合培养，获得2017年度国家青年科学基金、江苏省青年科学基金、江苏省教育厅高校自然科学基金。

★张清山获得2015年度博士生国家奖学金、2016年度国家青年科学基金、2017年度江苏省优秀博士论文。

社会活动

美国数学评论员。

数学期刊审稿人。

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