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，激波问题

讲授课程：

【本科生课程】

数学分析，2024

微积分CI，2022，2023

微分方程(双语/英语授课)，2011，2013，2014，2016，2017，2018，2019，2020

高等数学I(双语/英语授课)，2016

复变函数，2017，2018

单变量微积分(双语/英语授课)，2019

线性代数(英语授课)，2011

【研究生课程】

双曲守恒律组及其应用，2022，2023

学科专业外语，2023，2024

双曲守恒律方程(组) (英语授课)，2015，2017，2018

二阶抛物型微分方程(英语授课)，2015

数理方程(英语授课)，2019

教育经历：

2007.09 - 2010.08 香港中文大学，应用数学，博士

2005.08 - 2007.08 香港中文大学，应用数学，硕士

2001.09 - 2005.07 吉林大学，数学与应用数学，学士

工作经历：

2021.09 - 今  吉林大学数学学院，教授

2015.01 - 2016.01 曼海姆大学（德国），访问学者

2014.07 - 2021.09 大连理工大学数学学院，副教授/教授

2011.10 - 2014.07 浦项科技大学（韩国），研究助理教授

2010.09 - 2011.09 叶史瓦大学（美国），博士后

科研项目：

【主持国家自然科学基金项目】

[1]可压缩欧拉-泊松方程组解的适定性，面上项目，47万，2023-2026

[2]欧拉-泊松方程组跨音速课题的若干数学问题，面上项目，53万，2019-2022

[3]管道中欧拉-泊松流体的适定性问题，青年科学基金项目，18万，2016-2018

学术论文：

[1] Duan, Ben; Xing, Yuanyuan; Zheng, Haoran. Non-uniqueness of transonic shock solutions to Euler-Poisson system with varying background charges. Commun. Math. Sci.22(2024), no.3, 777–788.

[2] Duan, Ben; Li, Yutian; Lu, Dawei; Lu, Yang; Zhang, Ran. Pricing stocks with trading volumes. CSIAM Trans. Appl. Math.5(2024), no.1, 1–17.

[3] Duan, Ben; Xing, Yuanyuan; Zhou, Yan. Sonic-supersonic-shock-subsonic-sonic solution to Euler-Poisson system with varying background charges. Appl. Math. Lett.149(2024), Paper No. 108902, 6 pp.

[4] Duan, Ben; Wang, Chunpeng; Xing, Yuanyuan. Supersonic Euler-Poisson flows in divergent nozzles. J. Differential Equations 371(2023), 598–628.

[5] Duan, Ben; Luo, Zhen; Xing, Yuanyuan. Radial transonic shock solutions to Euler-Poisson system with varying background charge in an annulus. CSIAM Trans. Appl. Math.4(2023), no.1, 129–156.

[6] Duan, Ben; Lan, Ao; Luo, Zhen. Transonic Shock Solutions to the Euler System in Divergent-Convergent Nozzles. Acta Math. Sci. Ser. B (Engl. Ed.) 42 (2022), no. 4, 1536–1546. 35 (76).

[7] 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.

[8] 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.

[9] 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.

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

[11] 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.

[12] 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.

[13] 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.

[14] 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.

[15] 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.

[16] 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.

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

[18] 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.

[19] 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.

[20] 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.

[21] 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.

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

[23] 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.

[24] 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.

[25] 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.

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