赖耕
赖耕, 数学系副主任/副教授
电子邮箱:laigeng atshu.edu.cn
电话:021-6613xxxx
研究领域:
非线性双曲守恒律方程组的理论及应用,如二维黎曼问题、气体向真空扩散、激波反射、管道流、超声速射流、爆轰波、van der Waals气体基本波的相互作用等中的数学问题。曾获上海市自然科学二等奖(3/3)、古天乐代言太阳集团蔡冠深优秀青年教师奖、古天乐代言太阳集团吴兴华数学奖。
教育经历:
1. 2007年9月—2010年7月 古天乐代言太阳集团数学系(博士,导师:盛万成教授)
2. 2008年9月—2009年8月 宾夕法尼亚州立大学数学系(国家留学基金委联培项目,导师:郑玉玺教授)
3. 2004年9月—2007年7月 古天乐代言太阳集团数学系(硕士,导师:盛万成教授)
4. 2000年9月—2004年7月 古天乐代言太阳集团数学、物理、力学综合班(学士)
工作经历:
1. 2016年3月— 今 古天乐代言太阳集团数学系(副教授)
2. 2012年7月—2016年3月 古天乐代言太阳集团数学系(讲师)
3. 2010年7月—2012年7月 复旦大学数学科学学院(博士后,合作导师:李大潜院士)
代表性科研项目:
1. 上海市自然科学基金面上项目,非线性双曲守恒律方程组的二维黎曼问题及相关问题,2023/4/1–2026/3/31,主持
2. 国家自然科学基金面上项目,可压欧拉方程组的二维黎曼问题及一些相关问题的研究,2021/1–2024/12,主持
3. 国家自然科学基金青年项目,可压流Euler方程组的黎曼问题,2014/01–2016/12,主持
4. 上海市自然科学青年基金项目,反应流体Euler方程组及相关模型的Riemann问题, 2013/10–2016/9,主持
代表性学术论文:
1. G. Lai, Three-dimensional stationary supersonic flows with axial symmetry in relativistic hydrodynamics, J. Lond. Math. Soc. 108 (2023) 702-741.
2. G. Lai and W.C. Sheng, Supersonic reacting jet flows from a three-dimensional divergent conical nozzle, SIAM J. Math. Anal. 55 (2023) 5260-5317.
3. G. Lai, Sonic-supersonic jet flows from a two-dimensional nozzle, J. Differential Equations 360 (2023) 287–313.
4. G. Lai, Interactions of rarefaction waves and rarefaction shocks of the two-dimensional compressible Euler Equations with general equation of state, J. Dyn. Diff. Equat. 35 (2023) 381-419.
5. G. Lai, Spherical detonation waves in relativistic hydrodynamics, Physica D. 443 (2023) No. 133569, 18 pp.
6. G. Lai, Global solution to a three-dimensional spherical piston problem for the relativistic Euler equations, Europ. J. Appl. Math. 33 (2022) 1-26.
7. G. Lai and W.C. Sheng, Two-dimensional pseudo-steady flows around a sharp corner, Arch. Ration. Mech. Anal. 241 (2021) 805-884.
8. G. Lai, Global continuous sonic-supersonic flows in two-dimensional semi-infinite divergent ducts, J. Math. Fluid. Mech. 23 (2021) 77.
9. J.J. Chen and G. Lai, Self-similar solutions of the spherically symmetric Euler equations for general equations of state, Comm. Math. Sci. 19 (2021) 1991-2018
10. G. Lai, Self-similar solutions of the radially symmetric relativistic Euler equations, Europ. J. Appl. Math. 31 (2020) 919-949.
11. G. Lai, Global non-isentropic rotational supersonic flows in a semi-infinite divergent duct, SIAM J. Math. Anal. 52 (2020) 5121-5154.
12. G. Lai, Global solutions to a class of two-dimensional Riemann problems for the Euler equations with a general equation of state, Indiana Univ. Math. J. 68 (2019) 1409-1464.
13. G. Lai, Detonation wave solution to a 1D piston problem for the Zeldovich-von Neumann-Döring combustion model, J. Differential Equations 267 (2019) 4949-4974.
14. G. Lai, Interactions of composite waves of the two-dimensional full Euler equations for van der Waals gases, SIAM J. Math. Anal. 50 (2018) 3535-3597.
15. G. Lai, Interaction of fan-jump-fan composite waves in a two-dimensional steady jet for van der Waals gases, J. Hyperbolic Differ. Equ. 14 (2017) 73-134.
16. G. Lai and W.C. Sheng, Elementary wave interactions to the compressible Euler equations for Chaplygin gas in two dimensions, SIAM J. Appl. Math. 76 (2016) 2218-2242.
17. G. Lai and W.C. Sheng, Two-dimensional centered wave flow patches to the Guderley Mach reflection configurations for steady flows in gas dynamics, J. Hyperbolic Differ. Equ. 13 (2016) 107-128.
18. G. Lai, On the expansion of a wedge of van der Waals gas into a vacuum II, J. Differential Equations 260 (2016) 3538-3575.
19. G. Lai, On the expansion of a wedge of van der Waals gas into a vacuum, J. Differential Equations 259 (2015) 1181-1202.
20. G. Lai and W.C. Sheng, Centered wave bubbles with sonic boundary of pseudosteady Guderley Mach reflection configurations in gas dynamics, J. Math. Pures Appl. 104 (2015) 179-206.
21. G. Lai, On the Riemann problem for a scalar Zeldovich-von Neumann-Döring combustion model, SIAM J. Math. Anal. 46 (2014) 2404-2443.
22. G. Lai and W.C. Sheng, Nonexistence of the von Neumann reflection configuration for the triple point paradox, SIAM J. Appl. Math. 71 (2011) 2072-2092.
23. G. Lai, W.C. Sheng and Y.X. Zheng, Simple waves and pressure delta waves for a Chaplygin gas in two-dimensions, Discrete Contin. Dyn. Syst. 31 (2011) 489-523.
最后更新日期:2024.1.28
赖耕
赖耕, 数学系副主任/副教授
电子邮箱:laigeng atshu.edu.cn
电话:021-6613xxxx
研究领域:
非线性双曲守恒律方程组的理论及应用,如二维黎曼问题、气体向真空扩散、激波反射、管道流、超声速射流、爆轰波、van der Waals气体基本波的相互作用等中的数学问题。曾获上海市自然科学二等奖(3/3)、古天乐代言太阳集团蔡冠深优秀青年教师奖、古天乐代言太阳集团吴兴华数学奖。
教育经历:
1. 2007年9月—2010年7月 古天乐代言太阳集团数学系(博士,导师:盛万成教授)
2. 2008年9月—2009年8月 宾夕法尼亚州立大学数学系(国家留学基金委联培项目,导师:郑玉玺教授)
3. 2004年9月—2007年7月 古天乐代言太阳集团数学系(硕士,导师:盛万成教授)
4. 2000年9月—2004年7月 古天乐代言太阳集团数学、物理、力学综合班(学士)
工作经历:
1. 2016年3月— 今 古天乐代言太阳集团数学系(副教授)
2. 2012年7月—2016年3月 古天乐代言太阳集团数学系(讲师)
3. 2010年7月—2012年7月 复旦大学数学科学学院(博士后,合作导师:李大潜院士)
代表性科研项目:
1. 上海市自然科学基金面上项目,非线性双曲守恒律方程组的二维黎曼问题及相关问题,2023/4/1–2026/3/31,主持
2. 国家自然科学基金面上项目,可压欧拉方程组的二维黎曼问题及一些相关问题的研究,2021/1–2024/12,主持
3. 国家自然科学基金青年项目,可压流Euler方程组的黎曼问题,2014/01–2016/12,主持
4. 上海市自然科学青年基金项目,反应流体Euler方程组及相关模型的Riemann问题, 2013/10–2016/9,主持
代表性学术论文:
1. G. Lai, Three-dimensional stationary supersonic flows with axial symmetry in relativistic hydrodynamics, J. Lond. Math. Soc. 108 (2023) 702-741.
2. G. Lai and W.C. Sheng, Supersonic reacting jet flows from a three-dimensional divergent conical nozzle, SIAM J. Math. Anal. 55 (2023) 5260-5317.
3. G. Lai, Sonic-supersonic jet flows from a two-dimensional nozzle, J. Differential Equations 360 (2023) 287–313.
4. G. Lai, Interactions of rarefaction waves and rarefaction shocks of the two-dimensional compressible Euler Equations with general equation of state, J. Dyn. Diff. Equat. 35 (2023) 381-419.
5. G. Lai, Spherical detonation waves in relativistic hydrodynamics, Physica D. 443 (2023) No. 133569, 18 pp.
6. G. Lai, Global solution to a three-dimensional spherical piston problem for the relativistic Euler equations, Europ. J. Appl. Math. 33 (2022) 1-26.
7. G. Lai and W.C. Sheng, Two-dimensional pseudo-steady flows around a sharp corner, Arch. Ration. Mech. Anal. 241 (2021) 805-884.
8. G. Lai, Global continuous sonic-supersonic flows in two-dimensional semi-infinite divergent ducts, J. Math. Fluid. Mech. 23 (2021) 77.
9. J.J. Chen and G. Lai, Self-similar solutions of the spherically symmetric Euler equations for general equations of state, Comm. Math. Sci. 19 (2021) 1991-2018
10. G. Lai, Self-similar solutions of the radially symmetric relativistic Euler equations, Europ. J. Appl. Math. 31 (2020) 919-949.
11. G. Lai, Global non-isentropic rotational supersonic flows in a semi-infinite divergent duct, SIAM J. Math. Anal. 52 (2020) 5121-5154.
12. G. Lai, Global solutions to a class of two-dimensional Riemann problems for the Euler equations with a general equation of state, Indiana Univ. Math. J. 68 (2019) 1409-1464.
13. G. Lai, Detonation wave solution to a 1D piston problem for the Zeldovich-von Neumann-Döring combustion model, J. Differential Equations 267 (2019) 4949-4974.
14. G. Lai, Interactions of composite waves of the two-dimensional full Euler equations for van der Waals gases, SIAM J. Math. Anal. 50 (2018) 3535-3597.
15. G. Lai, Interaction of fan-jump-fan composite waves in a two-dimensional steady jet for van der Waals gases, J. Hyperbolic Differ. Equ. 14 (2017) 73-134.
16. G. Lai and W.C. Sheng, Elementary wave interactions to the compressible Euler equations for Chaplygin gas in two dimensions, SIAM J. Appl. Math. 76 (2016) 2218-2242.
17. G. Lai and W.C. Sheng, Two-dimensional centered wave flow patches to the Guderley Mach reflection configurations for steady flows in gas dynamics, J. Hyperbolic Differ. Equ. 13 (2016) 107-128.
18. G. Lai, On the expansion of a wedge of van der Waals gas into a vacuum II, J. Differential Equations 260 (2016) 3538-3575.
19. G. Lai, On the expansion of a wedge of van der Waals gas into a vacuum, J. Differential Equations 259 (2015) 1181-1202.
20. G. Lai and W.C. Sheng, Centered wave bubbles with sonic boundary of pseudosteady Guderley Mach reflection configurations in gas dynamics, J. Math. Pures Appl. 104 (2015) 179-206.
21. G. Lai, On the Riemann problem for a scalar Zeldovich-von Neumann-Döring combustion model, SIAM J. Math. Anal. 46 (2014) 2404-2443.
22. G. Lai and W.C. Sheng, Nonexistence of the von Neumann reflection configuration for the triple point paradox, SIAM J. Appl. Math. 71 (2011) 2072-2092.
23. G. Lai, W.C. Sheng and Y.X. Zheng, Simple waves and pressure delta waves for a Chaplygin gas in two-dimensions, Discrete Contin. Dyn. Syst. 31 (2011) 489-523.
最后更新日期:2024.1.28