非线性发展方程，如趋化方程，相场方程等

   

070104-应用数学
070101-基础数学

非线性发展方程

2004-09--2009-06   复旦大学数学科学学院   博士 （导师：郑宋穆教授）
2000-09--2004-06   山东大学数学与系统科学学院   学士

• 2004-2009，复旦大学数学科学学院
• 2000-2004，山东大学数学与系统科学学院
• 1997-2000，山东省实验中学
• 1994-1997，济南实验初级中学
• 1988-1994，济南师范学校附属小学

• 2022.12至今，中国科学院精密测量科学与技术创新研究院，数学及应用研究部，研究员

• 2013-10 至2022.11，中国科学院精密测量科学与技术创新研究院（原中国科学院武汉物理与数学研究所），数学及应用研究部, 副研究员

              其间：2014-07 至2015-08，美国宾夕法尼亚州立大学, 数学系, 访问学者（受柳春教授邀请，国家留学基金委公派访问学者项目资助）

• 2011-12 至2013-09, 中国科学院武汉物理与数学研究所, 数学物理与应用研究部, 助理研究员

  其间：2012-12 至2013-01, 日本东京大学, 数学系, 访问学者（受Yoshikazu Giga教授邀请，东京大学FMSP Lectures 项目资助）

• 2009-09 至2011-11, 北京应用物理与计算数学研究所，博士后 （合作导师：郭柏灵院士）

2025-06-01-今,湖北省数学学会, 常务理事
2023-07-20-今,AIMS Mathematics 编委,

   

（1） 中国科学院武汉教育基地优秀研究生指导教师, 研究所（学校）, 2025
（2） 湖北省工业与应用数学学会第一届优秀青年学者奖, 其他, 2023
（3） 2021年度精密测量院突出科技成果, 研究所（学校）, 2021
（4） 上海市优秀博士学位论文, 省级, 2011

     

Analysis on Chemotaxis Models

1.  A. Lu ad J. Jiang. Suppression of blowup by slightly superlinear degradation in a parabolic–elliptic Keller–Segel system with signal-dependent motility. Nonliner Analysis: Real World Applications, 2025, 81: 104190. https://doi.org/10.1016/j.nonrwa.2024.104190
2. Y. Xiao and J. Jiang. Prevention of infinite-time blowup by slightly super-linear degradation in a Keller–Segel system with density-suppressed motility. Nonlinearity, 2024, 37: 095007. 10.1088/1361-6544/ad6113
3. J. Jiang and P. Laurençot. Global bounded classical solutions to a parabolic-elliptic chemotaxis model with local sensing and asymptotically unbounded motility.  Bulletin of the London Mathematical Society, 2024, 56, 681-700.  https://doi.org/10.1112/blms.12958
4. Y. Xiao and J. Jiang. Global existence and uniform boundedness in a fully parabolic Keller-Segel system with non-monotonic signal-dependent motility. Journal of Differential Equations, 2023, 354, 403-429. https://doi.org/10.1016/j.jde.2023.02.028
5. J. Jiang*. On a repulsion Keller-Segel system with a logarithmic sensitivity. European Journal of Applied Mathematics, 2022, 33: 153-181. https://doi.org/10.1017/S0956792520000443
6. J. Jiang*. Boundedness and Exponential Stabilization in a Parabolic-Elliptic Keller-Segel Model with Signal-dependent Motilities for Local Sensing Chemotaxis. Acta Mathematica Scientia, 2022, 42B(3): 825-846. https://doi.org/10.1007/s10473-022-0301-y
7. J. Jiang, P. Laurençot*, and Y. Zhang. Global existence, uniform boundedness, and stabilization in a chemotaxis system with density-suppressed motility and nutrient consumption. Communications in Partial Differential Equations, 2022, 47(5): 1024-1069. https://doi.org/10.1080/03605302.2021.2021422
8.  K. Fujie* and J. Jiang. A note on construction of nonnegative initial data inducing unbounded solutions to some two-dimensional Keller–Segel systems. Mathematics in Engineering, 2021, 4(6): 1-12. 10.3934/mine.2022045
9.  K. Fujie and J. Jiang*. Boundedness of classical solutions to a degenerate Keller-Segel type model with signal-dependent motilities. Acta Applicandae Mathematicae, 2021, 176: 3. https://doi.org/10.1007/s10440-021-00450-1 (ESI Highly Cited Paper)
10. K. Fujie and J. Jiang*. Comparison methods for a Keller-Segel-type model of pattern formations with density-suppressed motilities. Calculus of Variations and Partial Differential Equations, 2021, 60: 92. https://doi.org/10.1007/s00526-021-01943-5  (ESI Highly Cited Paper & Hot Paper)
11. J. Jiang* and P. Laurençot. Global existence and uniform boundedness in a chemotaxis model with signal-dependent motility. Journal of Differential Equations, 2021, 299: 513-541. https://doi.org/10.1016/j.jde.2021.07.029 (ESI Highly Cited Paper)
12. H. Li and J. Jiang*. Global existence of weak solutions to a signal-dependent Keller-Segel model for local sensing chemotaxis. Nonlinear Analysis: Real World Applications, 2021, 61: 103338. https://doi.org/10.1016/j.nonrwa.2021.103338
13. K. Fujie and J. Jiang*. Global existence for a kinetic model of pattern formation with density-suppressed motilities. Journal of Differential Equations, 2020, 269(6): 5338-5378. https://doi.org/10.1016/j.jde.2020.04.001 (ESI Highly Cited Paper)
14. J. Jiang*. Global stability of Keller-Segel systems in critical Lebesgue spaces. Discrete & Continuous Dynamical Systems - A, 2020, 40(1): 609-634. 10.3934/dcds.2020025
15. J. Jiang*. Global stability of homogeneous steady states in scaling-invariant spaces for a Keller-Segel-Navier-Stokes system. Journal of Differential Equations, 2019, 267(2): 659-692. https://doi.org/10.1016/j.jde.2019.01.022
16. J. Jiang*. Eventual smoothness and exponential stabilization of global weak solutions to some chemotaxis systems. SIAM Journal on Mathematical Analysis, 2019, 51(6): 4604-4644. https://doi.org/10.1137/19M1245025
17. J. Jiang*. Convergence to equilibria of global solutions to a degenerate quasilinear Keller-Segel system. Zeitschrift für Angewandte Mathematik und Physik, 2018, 69(5). https://doi.org/10.1007/s00033-018-1025-7
18. J. Jiang*, H. Wu, and S. Zheng. Blow-up for a three dimensional Keller-Segel model with consumption of chemoattractant. Journal of Differential Equations, 2018, 264(8): 5432-5464. https://doi.org/10.1016/j.jde.2018.01.004
19. ‍‍J. Jiang*, H. Wu, and S. Zheng. Global existence and asymptotic behavior of solutions to a chemotaxis–fluid system on general bounded domains. Asymptotic Analysis, 2015, 92(3-4): 249-258. DOI: 10.3233/ASY-141276
20. J. Jiang* and Y. Zhang. On convergence to equilibria for a chemotaxis model with volume-filling effect. Asymptotic Analysis, 2009, 65(1-2): 79-102. DOI: 10.3233/ASY-2009-0948

Analysis on Phase Field Models

1. J. Jiang*, Y. Li, and C. Liu. Two-phase incompressible flows with variable density: An energetic variational approach. Discrete & Continuous Dynamical Systems - A, 2017, 37(6): 3243-3284. http://dx.doi.org/10.3934/dcds.2017138
2. J. Jiang*, H. Wu, and S. Zheng. Well-posedness and long-time behavior of a non-autonomous Cahn–Hilliard–Darcy system with mass source modeling tumor growth. Journal of Differential Equations, 2015, 259(7): 3032-3077. https://doi.org/10.1016/j.jde.2015.04.009
3. J. Jiang*. Long-time behaviour of solutions to a one-dimensional strongly nonlinear model for phase transitions with micro-movements. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2012, 142(6): 1279-1307. https://doi.org/10.1017/S0308210511000229
4. J. Jiang* and B. Guo. Asymptotic behavior of solutions to a one-dimensional full model for phase transitions with microscopic movements. Discrete & Continuous Dynamical Systems - A, 2012, 32(1): 167-190. 10.3934/dcds.2012.32.167
5. J. Jiang* and Y. Zhang. Counting the set of equilibria for a one-dimensional full model for phase transitions with microscopic movements. Quarterly of Applied Mathematics, 2012, 70: 665-683. https://www.ams.org/journals/qam/2012-70-04/S0033-569X-2012-01257-3/S0033-569X-2012-01257-3.pdf
6. J. Jiang*. Convergence to equilibrium for a fully hyperbolic phase-field model with Cattaneo heat flux law. Mathematical Methods in the Applied Sciences, 2009, 32(9): 1156-1182. https://doi.org/10.1002/mma.1092
7. J. Jiang*. Convergence to equilibrium for a parabolic–hyperbolic phase field model with Cattaneo heat flux law. Journal of Mathematical Analysis and Applications, 2008, 341(1): 149-169. https://doi.org/10.1016/j.jmaa.2007.09.041

Others

1. J. Jiang* and S. Zheng. Global well-posedness and exponential stability of solutions for the viscous radiative and reactive gas. Zeitschrift für angewandte Mathematik und Physik, 2014, 65(4): 645-686. https://doi.org/10.1007/s00033-013-0350-0
2. H. Wu* and J. Jiang. Global solution to the drift-diffusion-Poisson system for semiconductors with nonlinear recombination-generation rate. Asymptotic Analysis, 2013, 85(1-2): 75-105. DOI: 10.3233/ASY-131176
3. J. Jiang* and S. Zheng. Global solvability and asymptotic behavior of a free boundary problem for the one-dimensional viscous radiative and reactive gas. Journal of Mathematical Physics, 2012, 53: 123704. https://doi.org/10.1063/1.4770049
4. J. Jiang, H. Wu*, and B. Guo. Finite dimensional global and exponential attractors for a class of coupled time-dependent Ginzburg-Landau equations. Science China Mathematics, 2011, 55(1): 141-157. https://doi.org/10.1007/s11425-011-4229-2

 

‍‍‍‍

J. Jiang and Ph. Laurençot, Global boundedness induced by asymptotically non-degenerate motility in a fully parabolic chemotaxis model with local sensing. arxiv

• 中国科学院PIFI国际访问学者项目，负责人，2024.10--2025.12，结题。PIFI Story
• 系数依赖信号的Keller-Segel趋化方程的数学研究，负责人，国家自然科学基金面上项目，2023-01--2026-12，在研
• 传染病时空传播动力学建模与分析, 负责人, 中科院精密测量院多学科交叉培育项目, 2021-12--2023-11，已结题
• 具有动力边界条件的Cahn-Hilliard方程及其与流体耦合系统的数学分析, 参与, 国家自然科学基金面上项目, 2021-01--2024-12，已结题
• 一类退化型生物趋化方程的数学研究, 负责人, 湖北省自然科学基金面上项目, 2020-03--2022-03，已结题
• 复杂流体中几类非线性发展方程组的适定性与渐近性态, 参与, 国家自然科学基金面上项目, 2014-01--2017-12，已结题
• Frémond相变热力学模型发展方程组整体解及其渐近性态, 负责人, 国家自然科学基金青年基金项目, 2013-01--2015-12，已结题

• International Conference on Mathematical Modeling in Biology: From Chemotaxis to Complex Systems, 2025.09.24-26, KAIST, Daejeon, Repuplic of Korea,  40min, Conference Webpage.

• Institute of Mathematics, Vietnam Academy of Science and Technology,  2025.06.17, 1hour, online talk
• 偏微分方程理论分析与应用研讨会，烟台大学，2025.05.30-06.02，30min
• 京港澳应用数学学科发展与人才培养合作交流学术会议，北京工业大学，2025.05.21-05.23，30min
• 第十二届偏微分方程青年学术论坛，山西大学，2025.05.09-05.12，30min
• 2025 年春季反应扩散方程研讨会，华南理工大学，2025.03.28-03.31，35min
• 分析学前沿学术论坛，武汉大学，2025.2.27, 40min
• 反应扩散方程研讨会 V，上海交通大学，2024.11.30-12.1，35min
• 湖北省数学学会2024年学术年会，襄阳，2024.11.1-11.3, 40min.
• 反应扩散方程青年学者专题报告会，浙江师范大学，2024.10.27-10.29，30min.
• 2024年东南大学反应扩散方程研讨会，东南大学，2024.10.19-10.20, 40min
• 2024 数学物理中偏微分方程理论及其应用, 北京应用物理与计算数学研究所，2024.10.19， 30min
• PDEs Models of Mathematical Biology,  The Hong Kong Polytechnic University, 2024.09.27, 40min. 
• 2024数学物理方程与可积系统学术研讨会，江苏大学， 2024.06.22-06.23，"Prevention of Infinite-time Blowup by Slightly Super-linear Degradation in a Keller--Segel System with Density-suppressed Motility", 30min.
• 2024年夏季反应扩散方程学术会议(西安)，西北工业大学，2024.05.11-05.12，"Prevention of Infinite-time Blowup by Slightly Super-linear Degradation in a Keller--Segel System with Density-suppressed Motility", 40min. 
• The 7th International Workshop on Mathematical Analysis of Chemotaxis, Kyoto University of Education, 2024.03.04-2024.03.08, "Some Recent Progress in a Parabolic-Elliptic Keller--Segel System with Signal-dependent Motility", 60min.  Conference Webpage.
• 2023 东华大学天元吸引子高级研讨班，东华大学，2023.06.17-06.18，"On a parabolic-elliptic Keller-Segel system with signal-dependent motility", 45min
• 东北偏微分方程小型研讨会，大连理工大学，2023.06.15-06.16，“The Effect of Signal-dependent Motility in a Keller--Segel System"，35min
• 华南师大2023 年春季偏微分方程系列报告会，华南师范大学，2023.04.15-04.16，"On a Parabolic-Elliptic Keller-Segel System with Signal-dependent Motility", 40min
• 2022非线性偏微分方程理论及应用研讨会，厦门理工学院，2022.11.26，“The Effect of Signal-dependent Motility in a Keller--Segel System of Chemotaxis”，45min
• 非线性偏微分方程系列报告，广州大学，2022.10.21, “The Effect of Signal-dependent Motility in a Keller-Segel System of Chemotaxis”, 30min
• 2022怪波与波湍流理论学术研讨会，西宁，2022.08.12-2022.08.14，"On a Keller-Segel system of chemotaxis with signal-dependent motility", 45min
• The 2nd International Workshop on Mathematical Analysis of Chemotaxis mini, online, Tokyo University of Science，2022.03.07-2022.03.09, "On a Keller-Segel System of Chemotaxis with Density-suppressed Motility", 30min
• 2021人民大学偏微分方程系列报告会4，online，2021.11.20，"On a Keller-Segel model with density-suppressed motility", 40min
• Online Workshop on Mathematical Biology, 2021.09.10, Online，University of Nottingham Ningbo China，"On a Keller-Segel System of Chemotaxis with Density-suppressed Motility", 50min

• 数学物理方程学术研讨会，青岛，2021.06.18-2021.06.20, "The Effect of Density-suppressed Motility in Some Reaction-Diffusion Systems", 30min

• 偏微分方程建模、理论与计算学术会议，厦门，2020.11.20-2020.11.23，"Comparison Methods for a Keller-Segel Model with Signal-dependent Motilities", 30min
• 2020年偏微分方程与动力系统学术研讨会，佛山，2020.11.6-2020.11.8，"On a Keller-Segel Model with Signal-dependent Motilities for Local Sensing Chemotaxis", 35min
• 湖北省工业与应用数学学会暨武汉工业与应用数学学会2020 年学术交流大会, 武汉，2020.09.18-2020.09.20, "On a Keller-Segel Model with Signal-dependent Motility for Local Sensing Chemotaxis", 25min

Editorial Board Member of AIMS Mathematics

Hao Wu（吴昊），Yanyan Zhang（张艳艳），Yinghua Li（李颖花），Chun Liu（柳春），Kentaro Fujie，Philippe Laureçot

在读：

孙玉娇，硕士研究生

已毕业：

李海霞，  硕士，论文（https://doi.org/10.1016/j.nonrwa.2021.103338），毕业去向：武汉市翠微中学

陆艾静，硕士, 论文（https://doi.org/10.1016/j.nonrwa.2024.104190），毕业去向：中国银行

• A letter from the frustrated author of a journal paper
• 数学传播
• 数学译林
• 数学文化
• 神经网络与深度学习
• Lean4, Lean4入门, online Lean playground, A slightly longer Lean 4 proof tour (by T. Tao)
• PDE可视化
• Quantamagazin