段犇

• 性别：男

  职称：教授

  所在系别：应用数学系

  是否博导：是

• 办公地点：成人直播平台 中心校区，伍卓群楼

  电子邮箱：[email protected]

• 偏微分方程、双曲守恒律方程组、流体动力学方程组、Euler及Euler-Poisson方程组、相对论量子场方程组

• 本科生课程：数学分析、微积分等
  研究生课程：学科专业外语、双曲守恒律组及其应用等

• 2007-2010 香港中文大学数学科学研究所 博士研究生
  2005-2007 香港中文大学数学科学研究所 硕士研究生
  2001-2005 成人直播平台 本科

• 2021-今 成人直播平台 教授
  2019-2021 大连理工大学成人直播平台 教授
  2015-2016 德国曼海姆大学 访问学者
  2014-2019 大连理工大学成人直播平台 副教授
  2011-2014 韩国浦项科技大学 研究助理教授
  2010-2011 美国叶史瓦大学 博士后

• [1] 高维非线性双曲方程（国家重点研发计划项目），课题（2024YFA1013303）：高维Euler-Poisson方程组的动力学行为和相关奇异极限，2024-2029，国家自然科学基金委员会高技术研究发展中心，课题负责人
  [2] 可压缩欧拉-泊松方程组解的适定性（面上，12271205），2023-2026，国家自然科学基金委，负责人
  [3] 欧拉-泊松方程组跨音速课题的若干数学问题（面上，11871133），2019-2022，国家自然科学基金委，负责人
  [4] 管道中欧拉-泊松流体的适定性问题（青年基金，11501077），2016-2018，国家自然科学基金，负责人

• [1] L. Du and B. Duan. Global subsonic Euler flows in an infinitely long axisymmetric nozzle. J. Differential Equations 250 (2011), no. 2, 813–847.
  [2] B. Duan and S. Weng. Transonic shock in finitely long nozzle with porous medium boundary condition. J. Differential Equations 251 (2011), no. 4-5, 1128–1156.
  [3] B. Duan, Z. Luo and Y. Zheng. Local existence of classical solutions to shallow water equations with Cauchy data containing vacuum. SIAM J. Math. Anal. 44 (2012), no. 2, 541–567.
  [4] B. Duan and Z. Luo. Three-dimensional full Euler flows in axisymmetric nozzles. J. Differential Equations 254 (2013), no. 7, 2705–2731.
  [5] M. Bae, B. Duan and C. Xie. Subsonic solutions for steady Euler-Poisson system in two-dimensional nozzles. SIAM J. Math. Anal. 46 (2014), no. 5, 3455–3480.
  [6] M. Bae, B. Duan and C. Xie. Two-dimensional subsonic flows with self-gravitation in bounded domain. Math. Models Methods Appl. Sci. 25 (2015), no. 14, 2721–2747.
  [7] M. Bae, B. Duan and C. Xie. Subsonic flow for the multidimensional Euler-Poisson system. Arch. Ration. Mech. Anal. 220 (2016), no. 1, 155–191.
  [8] J. Che, L. Chen, B. Duan and Z. Luo. 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] B. Duan and Y. Zhou. Non-isentropic multi-transonic solutions of Euler-Poisson system. J. Differential Equations 268 (2020), no. 11, 7029–7046.
  [10] B. Duan and Y. Xing. 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.
  [11] M. Bae, B. Duan, J. Xiao and C. Xie. Structural stability of supersonic solutions to the Euler-Poisson system. Arch. Ration. Mech. Anal. 239 (2021), no. 2, 679–731.
  [12] B. Duan and N. Zhang. Non-uniqueness of transonic shock solutions to non-isentropic Euler-Poisson system. Commun. Math. Sci. 19 (2021), no. 4, 903–917.
  [13] B. Duan, C. Wang and Y. Xing. Supersonic Euler-Poisson flows in divergent nozzles. J. Differential Equations 371 (2023), 598–628.
  [14] B. Duan, Z. Luo and Y. Xing. 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.
  [15] B. Duan, Y. Li, D. Lu, Y. Lu and R. Zhang. Pricing stocks with trading volumes. CSIAM Trans. Appl. Math.5 (2024), no.1, 1–17.
  [16] B. Duan, Y. Xing and H. Zheng. Non-uniqueness of transonic shock solutions to Euler-Poisson system with varying background charges. Commun. Math. Sci.22 (2024), no.3, 777–788.
  [17] B. Duan, Y. Xing, and Y. Zhou. Sonic-supersonic-shock-subsonic-sonic solution to Euler-Poisson system with varying background charges. Appl. Math. Lett.149 (2024), Paper No. 108902, 6 pp.
  [18] B. Duan, Z. Luo and C. Wang. Structural stability of non-isentropic Euler-Poisson system for gaseous stars. J. Differential Equations 417 (2025), 105–131.

• [1] 2021年 国家天元数学东北中心优秀青年学者
  [2] 2022年 成人直播平台 唐敖庆领军教授
  [3] 2022年 教育部高等学校科学研究优秀成果奖（科学技术）二等奖（第二完成人）