一、基本信息

姓名：宋先发

学位：理学博士

职称职务：专任教师

电子邮箱：songxianfa2004@163.com

研究方向：偏微分方程、变分法

二、学习经历与进校时间

1990.09-1994.06 吉首大学，数学系，本科

1994.07-1998.08  湖南省会同县第二中学，中学二级教师

1998.09-2003.12  大连理工大学，应用数学系，硕博连读

2004.01-2006.02  清华大学，数学科学系，博士后

2006.03-2008.05  中国矿业大学（北京），理学院院长助理，数学系系主任，副教授

2008.06-至今    天津大学，数学学院数学系，副教授

（2014/06-2015/06 Department of Mechanical Engineering, University of Houston, Visiting Scholar，美国休斯敦大学力学工程系，访问学者）

2025.08-至今    天津大学援建新疆工学院通识学院数学教研部专任教师

三、课题项目

1、主持项目（省部级）

中国博士后科学基金资助项目：爆破或淬火现象发生时非线性抛物型方程（组）解的估计，2005.09--2006.09.

2、参加项目（国家级）

(1). 国家自然科学基金项目：临界点理论及其在非线性偏微分方程中的应用，11071237，2011.01--2013.12;

(2). 国家自然科学基金项目：不变集理论及其应用中若干问题的研究, 11471240，2015.01--2018.12。

3、教改项目

《非线性数学（上、下）》课程教改，YCX16019.

三、论文/专著/专利

迄今为止，已在国际数学SCI期刊上发表论文三十多篇，总共被SCI引用三百多次，单篇最高被引用次数46次。

1、An, Xiaowei; He, Huixia; Song, Xianfa,  Liouville type theorem and Morse indices of a semilinear elliptic equation with nonlocal nonlinearities, J. Math. Phys. 64 (2023), no. 5, Paper No. 051501, 11 pp.

2、Bao, Aiguo; Song, Xianfa, Lower bound for the blowup time of the solution to a quasi-linear parabolic system, J. Math. Phys. 62 (2021), no. 12, Paper No. 123504, 7 pp.

3、 An, Xiaowei; Song, Xianfa, A spatial SIS model in heterogeneous environments with vary advective rate, Math. Biosci. Eng. 18 (2021), no. 5, 5449–5477.

4、Hu, Yuanyang; Hao, Xinan; Song, Xianfa; Du, Yihong,  A free boundary problem for spreading under shifting climate, J. Differential Equations 269 (2020), no. 7, 5931–5958.

5、Zhang, Lin; Song, Xianfa, Global asymptotic behavior of solutions to quasilinear Schrödinger equations,

Electron. J. Differential Equations 2020, Paper No. 27, 14 pp.

6、Song, Xianfa, Some results on the Gierer-Meinhardt model with critical exponent  p−1=r,

Appl. Math. Lett. 106 (2020), 106348, 6 pp.

7、Song, Xianfa; Lv, Xiaoshuang, The relationships between some types of partial differential equations and ordinary differential equations as well as their applications, Math. Methods Appl. Sci. 41 (2018), no. 5, 2152–2161.

8、An, Xiaowei; He, Zhen; Song, Xianfa,The explicit solution to the initial-boundary value problem of Gierer-Meinhardt model, Appl. Math. Lett. 80 (2018), 59–63.

9、Peng, Rui; Song, Xianfa; Wei, Lei,  Existence, nonexistence and uniqueness of positive stationary solutions of a singular Gierer-Meinhardt system, Discrete Contin. Dyn. Syst. 37 (2017), no. 8, 4489–4505.

10、An, Xiaowei; Song, Xianfa, The lower bound for the blowup time of the solution to a quasi-linear parabolic problem, Appl. Math. Lett. 69 (2017), 82–86.

11、Lu, Jing; Bao, Aiguo; Song, Xianfa, Estimates on the blowup time for a quasilinear parabolic system,

Appl. Anal. 96 (2017), no. 4, 652–662.

12、Li, Fang; Peng, Rui; Song, Xianfa, Global existence and finite time blow-up of solutions of a Gierer-Meinhardt system,  J. Differential Equations 262 (2017), no. 1, 559–589.

13、Bao, Aiguo; Song, Xianfa, Bounds for the blowup time of the solution to a parabolic system with nonlocal factors in nonlinearities,  Comput. Math. Appl. 71 (2016), no. 3, 723–729.

14、Wang, Ning; Song, Xianfa; Lv, Xiaoshuang, Estimates for the blowup time of a combustion model with nonlocal heat sources, J. Math. Anal. Appl. 436 (2016), no. 2, 1180–1195.

15、Song, Xianfa; Lv, Xiaoshuang, Bounds for the blowup time and blowup rate estimates for a type of parabolic equations with weighted source, Appl. Math. Comput. 236 (2014), 78–92.

16、Lv, Xiaoshuang; Song, Xianfa, Bounds of the blowup time in parabolic equations with weighted source under nonhomogeneous Neumann boundary condition, Math. Methods Appl. Sci. 37 (2014), no. 7, 1019–1028.

17、Bao, Aiguo; Song, Xianfa, Bounds for the blowup time of the solutions to quasi-linear parabolic problems, Z. Angew. Math. Phys. 65 (2014), no. 1, 115–123.

18、An, Xiaowei; Li, Desheng; Song, Xianfa,  Phenomena of blowup and global existence of the solution to a nonlinear Schrödinger equation, Abstr. Appl. Anal. 2013, Art. ID 238410, 14 pp.

19、An, Xiaowei; Song, Xianfa, A note on blow-up analysis for a system of semilinear parabolic equations,

Nonlinear Anal. Real World Appl. 12 (2011), no. 1, 611–614.

20、Song, Xianfa; Zhao, Lin, Gradient estimates for the elliptic and parabolic Lichnerowicz equations on compact manifolds, Z. Angew. Math. Phys. 61 (2010), no. 4, 655–662.

21、Ma, Li; Song, Xianfa; Zhao, Lin, New monotonicity formulae for semi-linear elliptic and parabolic systems, Chinese Ann. Math. Ser. B 31 (2010), no. 3, 411–432.

22、An, Xiaowei; Song, Xianfa, Blow-up rate estimates for a parabolic system with multiple nonlinearities,

Math. Methods Appl. Sci. 33 (2010), no. 5, 632–642.

23、Song, Xianfa, Sharp thresholds of global existence and blowup for a system of Schrödinger equations with combined power-type nonlinearities, J. Math. Phys. 51 (2010), no. 3, 033509, 21 pp.

24、Song, Xianfa, Stability and instability of standing waves to a system of Schrödinger equations with combined power-type nonlinearities, J. Math. Anal. Appl. 366 (2010), no. 1, 345–359.

25、Ma, Li; Song, Xianfa; Zhao, Lin, On global rough solutions to a non-linear Schrödinger system,

Glasg. Math. J. 51 (2009), no. 3, 499–511.

26、Song, Xianfa, Blow-up analysis for a system of heat equations with nonlinear flux which obey different laws, Nonlinear Anal. 69 (2008), no. 7, 1971–1980.

27、Zheng, SiNing; Song, XianFa, Quenching rates for heat equations with coupled singular nonlinear boundary flux, Sci. China Ser. A 51 (2008), no. 9, 1631–1643.

28、 Ma, Li; Zhao, Lin; Song, Xianfa, Gradient estimate for the degenerate parabolic equation  ut=ΔF(u)+H(u)  on manifolds,  J. Differential Equations 244 (2008), no. 5, 1157–1177.

29、Song, Xianfa, Blow-up analysis for a system of heat equations coupled via nonlinear boundary conditions, Math. Methods Appl. Sci. 30 (2007), no. 10, 1135–1146.

30、Song, Xianfa; Zheng, Sining; Jiang, Zhaoxin, Blow-up analysis for a nonlinear diffusion system,

Z. Angew. Math. Phys. 56 (2005), no. 1, 1–10.

31、Zheng, Sining; Liang, Wenmiao; Song, Xianfa, Critical exponents in a parabolic system with inner absorption and coupled nonlinear boundary flux, Appl. Math. Comput. 154 (2004), no. 2, 567–581.

32、Zheng, Sining; Song, Xianfa; Jiang, Zhaoxin, Critical Fujita exponents for degenerate parabolic equations coupled via nonlinear boundary flux, J. Math. Anal. Appl. 298 (2004), no. 1, 308–324.

33、Zheng, Sining; Song, Xianfa,  Interactions among multi-nonlinearities in a nonlinear diffusion system with absorptions and nonlinear boundary flux, Nonlinear Anal. 57 (2004), no. 4, 519–530.

34、Song, Xianfa; Zheng, Sining, Multinonlinear interactions in quasi-linear reaction-diffusion equations with nonlinear boundary flux, Math. Comput. Modelling 39 (2004), no. 2-3, 133–144.

35、Jiang, Zhaoxin; Zheng, Sining; Song, Xianfa, Blow-up analysis for a nonlinear diffusion equation with nonlinear boundary conditions,  Appl. Math. Lett. 17 (2004), no. 2, 193–199.

36、Song, Xianfa; Zheng, Sining, Blow-up analysis for a quasilinear parabolic system with multi-coupled nonlinearities,  J. Math. Anal. Appl. 281 (2003), no. 2, 739–756.

37、Song, Xianfa; Zheng, Sining, Blow-up and blow-up rate for a reaction-diffusion model with multiple nonlinearities,  Nonlinear Anal. 54 (2003), no. 2, 279–289.