songxianfa
School
School of Mathematics
Professional Title
Associate professor
Administrative Appointments
teacher
Contact Information
songxianfa@tju.edu.cn
Education Background
- Ph. D| Dalian University of Technology| Computational mathematics| 2003
- Bachelor of Science| Jishou University| Mathematics| 1994
Research Interests
- Partial Differential Equations
Positions & Employments
-
2008.6-2019.12
Department of Mathematics | Tianjin University -
2004.1-2006.2
Department of Mathematics | Tsinghua University -
2006.3-2008.6
Department of Mathematics | China University of Mining and Technology -
1994.7-1998.8
The Second Middle School of Huitong County
Academic Achievements
- Papers
- [1] 28.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.
- [2] 27.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.
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- [3] 26.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.
- [4] 25.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.
- [5] 24.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.
- [6] 23.heng, 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.
- [7] 22.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.
- [8] 21.Song, Xianfa; Zheng, Sining; Jiang, Zhaoxin Blow-up analysis for a nonlinear diffusion system. Z. Angew. Math. Phys. 56 (2005), no. 1, 1–10.
- [9] 20.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.
- [10] 19.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.
- [11] 18.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.
- [12] 17.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.
- [13] 16.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.
- [14] 15.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.
- [15] 14.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.
- [16] 13.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.
- [17] 12.Ma, Li; Song, Xianfa; Zhao, Lin New monotonicity formulae for semi-linear elliptic and parabolic systems. Chin. Ann. Math. Ser. B 31 (2010), no. 3, 411–432.
- [18] 11.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.
- [19] 10.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] 9.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.
- [21] 8.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.
- [22] 7.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.
- [23] 6.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.
- [24] 5.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.
- [25] 4.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.
- [26] 3.Li, Fang, Peng, Rui and 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.
- [27] 2.Lu, Jing, Bao, Aiguo and Song Xianfa, Estimates on the blowup time for a quasilinear parabolic system. Appl. Anal. 96 (2017), no. 4, 652–662.
- [28] 1.An, Xiaowei and 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.