段犇

性别：

男

职称：

教授

所在系别：

应用数学系

最高学历：

博士研究生

最高学位：

博士

Email：

bduan@jlu.edu.cn

所在学科业：

应用数学

所研究方向：

偏微分方程，双曲守恒律方程组，流体动力学方程组，Euler/Euler-Poisson 方程组，管道流体问题和激波问题

讲授课程：

微分方程，微积分，数学物理方程，双曲守恒律组

教育经历：

2007年09月-2010年08月 香港中文大学应用数学系博士

2005年08月-2007年08月 香港中文大学应用数学系硕士

2001年09月-2005年07月 必威官网学士

工作经历：

2021年9月-至今  必威官网教授

2019年12月-2021年09月 大连理工大学必威教授

2015年01月-2016年01月 曼海姆大学（德国）访问学者

2014年07月-2019年12月 大连理工大学必威教授

2011年10月-2014年07月 浦项科技大学（韩国）助理教授

2010年09月-2011年09月 Yeshiva大学（美国）博士后

科研项目：

1. 国家自然科学基金面上项目，欧拉-泊松方程组跨音速课题的若干数学问题，2019/01-2022/12, 在研，主持

2. 国家自然科学基金面上项目，具非局部效应反应扩散方程解的动力学行为，2022/01-2025/12, 在研，参与

3. 国家自然科学基金面上项目，可压缩流体方程组的若干数学理论研究，2017/01-2020/12, 结题，参与

4. 国家自然科学基金青年项目，管道中欧拉-泊松流体的适定性问题，2016/01-2018/12，结题，主持

学术论文：

[1] Duan, Ben; Zhang, Na Non-uniqueness of transonic shock solutions to non-isentropic Euler-Poisson system. Commun. Math. Sci. 19 (2021), no. 4, 903–917.

[2] Bae, Myoungjean; Duan, Ben; Xiao, Jingjing; Xie, Chunjing Structural stability of supersonic solutions to the Euler-Poisson system. Arch. Ration. Mech. Anal. 239 (2021), no. 2, 679–731.

[3] Duan, Ben; Xing, Yuanyuan The well-posedness of shock solutions to non-isentropic Euler-Poisson system with varying background charges. Z. Angew. Math. Phys. 71 (2020), no. 5, Paper No. 175, 12 pp.

[4] Duan, Ben; Zhou, Yan Non-isentropic multi-transonic solutions of Euler-Poisson system. J. Differential Equations 268 (2020), no. 11, 7029–7046.

[5] Duan, Ben; Luo, Zhen; Zhou, Yan Existence of strong solutions to the rotating shallow water equations with degenerate viscosities. Anal. Appl. (Singap.) 18 (2020), no. 2, 333–358.

[6] Duan, Ben; Luo, Zhen; Yan, Wei Finite-time blow-up of classical solutions to the rotating shallow water system with degenerate viscosity. Z. Angew. Math. Phys. 70 (2019), no. 2, Paper No. 54, 9 pp.

[7] Duan, Ben; Weng, Shangkun Global smooth axisymmetric subsonic flows with nonzero swirl in an infinitely long axisymmetric nozzle. Z. Angew. Math. Phys. 69 (2018), no. 5, Paper No. 135, 17 pp.

[8] Che, Jiahang; Chen, Li; Duan, Ben; Luo, Zhen On the existence of local strong solutions to chemotaxis–shallow water system with large data and vacuum. J. Differential Equations 261 (2016), no. 12, 6758–6789.

[9] Du, Lili; Duan, Ben Subsonic Euler flows with large vorticity through an infinitely long axisymmetric nozzle. J. Math. Fluid Mech. 18 (2016), no. 3, 511–530.

[10] Duan, Ben; Luo, Zhen; Xiao, Jingjing Transonic shock solutions to the Euler-Poisson system in quasi-one-dimensional nozzles. Commun. Math. Sci. 14 (2016), no. 4, 1023–1047.

[11] Bae, Myoungjean; Duan, Ben; Xie, Chunjing Subsonic flow for the multidimensional Euler-Poisson system. Arch. Ration. Mech. Anal. 220 (2016), no. 1, 155–191.

[12] Bae, Myoungjean; Duan, Ben; Xie, Chunjing Two-dimensional subsonic flows with self-gravitation in bounded domain. Math. Models Methods Appl. Sci. 25 (2015), no. 14, 2721–2747.

[13] Duan, Ben; Luo, Zhen Subsonic non-isentropic Euler flows with large vorticity in axisymmetric nozzles. J. Math. Anal. Appl. 430 (2015), no. 2, 1037–1057.

[14] Bae, Myoungjean; Duan, Ben; Xie, Chunjing Subsonic solutions for steady Euler-Poisson system in two-dimensional nozzles. SIAM J. Math. Anal. 46 (2014), no. 5, 3455–3480.

[15] Duan, Ben; Luo, Zhen Dynamics of vacuum states for one-dimensional full compressible Navier-Stokes equations. Commun. Pure Appl. Anal. 12 (2013), no. 6, 2543–2564.

[16] Duan, Ben; Luo, Zhen Three-dimensional full Euler flows in axisymmetric nozzles. J. Differential Equations 254 (2013), no. 7, 2705–2731.

[17] Duan, Ben; Luo, Zhen; Zheng, Yuxi Local existence of classical solutions to shallow water equations with Cauchy data containing vacuum. SIAM J. Math. Anal. 44 (2012), no. 2, 541–567.

[18] Du, Lili; Duan, Ben Note on the uniqueness of subsonic Euler flows in an axisymmetric nozzle. Appl. Math. Lett. 25 (2012), no. 2, 153–156.

[19] Duan, Ben; Weng, Shangkun Transonic shock in finitely long nozzle with porous medium boundary condition. J. Differential Equations 251 (2011), no. 4-5, 1128–1156.

[20] Du, Lili; Duan, Ben Global subsonic Euler flows in an infinitely long axisymmetric nozzle. J. Differential Equations 250 (2011), no. 2, 813–847.