梁兴  (教授)

梁兴中文简历.pdf

梁兴，中国科学技术大学数学科学学院教授，博士生导师。

 

1994年本科入学中国科学技术大学数学系，2003年获得理学博士学位，从事微分方程动力学，特别是扩散系统时空动力学及其应用的研究。

 

近年来与合作者在扩散系统传播理论、算子特征值问题方面取得进展：

(1)建立了单稳定扩散传播问题的动力系统研究理论，以此解决了该领域一些重要问题发表于CPAM的工作成为该杂志20年来引用率最高的论文之一。

(2)发展微分算子、积分算子的主特征值理论，给出主特征值的理论分析和算法。这一理论被广泛应用于传染病学的基本再生数（基本传染数）的理论和数值分析。

(3) 研究复杂介质中扩散传播问题，发现反常的传播现象，建立反应扩散方程与微分动力系统、遍历论、薛定谔算子谱理论的一些新联系。

相关工作接受发表在CPAM, Adv.Math, Math.Ann., JMPA, SIAM JMA等期刊。

 

其中发表于CPAM和JFA的工作已经成为抛物系统传播问题研究领域的基本文献，被广泛应用于具体偏微分方程和生态学、传染病学模型的研究传播问题研究。有些基本工作出乎意料地引起控制与优化、数学物理等方向学者，如ICM大会报告人Alberto Bressan等的实质性应用。

 

最近研究兴趣：非经典扩散系统奇异传播现象及其与不同数学学科的联系，例如均质化理论；非对称二阶椭圆算子谱与抛物方程传播现象；流形上抛物方程与解的几何；Levi flight生成的扩散系统与非局部扩散现象、行波解与动力系统不变叶层理论的联系。

主要论文目录 

1. X. Liang, T. Zhou, Estimate on exponential spreading speeds of Fisher-KPP equations with

fractional diffusion in heterogeneous media via generalized principal eigenvalues , Archive for

Rational Mechanics and Analysis. accepted, 2026

2. X. Liang, H. Wang, Q. Zhou, Almost-periodic ground state of the non-self-adjoint Jacobi

operator and its applications, Journal de Mathématiques Pures et Appliquées, 2026.

3. X. Liang, L. Xu, T. Zhou, Generalized principal eigenvalues of elliptic operators and spreading

speeds of Fisher-KPP equations in two-scale almost periodic media, arXiv preprint arXiv:2507.21870,

2025.10 

4. W. Ding, F. Hamel, X. Liang, Bistable pulsating fronts in slowly oscillating one-dimensional

environments, Journal de Mathématiques Pures et Appliquées, 2025.

5. W. Ding, X. Li, X. Liang, Time-periodic traveling waves and propagating terraces for multi-

stable equations with a fractional Laplacian: An abstract dynamical systems approach, Journal

of Functional Analysis 288(2), 2025.

6. X. Liang, L. Zhang, M. Zhang, The influence of advection on the propagation phenomena

of reaction-diffusion equations with KPP-bistable nonlinearity, Transactions of the American

Mathematical Society，379 (2026), 7703– 7756.

7. X. Liang, H. Wang, Q. Zhou, T. Zhou, Traveling fronts for Fisher–KPP lattice equations in

almost-periodic media, Annales de l’Institut Henri Poincaré C 41(5), 1179–1237, 2023.

8. W. Ding, X. Liang, Sign of the pulsating wave speed for the bistable competition–diffusion

system in a periodic habitat, Mathematische Annalen 385(3), 2023.

9. Y. Du, Y. Hu, X. Liang, A climate shift model with free boundary: enhanced invasion, Journal

of Dynamics and Differential Equations 35(1), 771–809, 2023.

10. X. Liang, T. Zhou, Propagation of KPP equations with advection in one-dimensional almost

periodic media and its symmetry, Advances in Mathematics 407, 108568, 2022.

11. X. Liang, T. Zhou, Spreading speeds of nonlocal KPP equations in heterogeneous media, Acta

Mathematica Sinica, English Series 38(1), 161–178, 2022.

12. X. Chen, X. Liang, J.-C. Tsai, Pulsating waves in a dissipative medium with Delta sources on

a periodic lattice, Journal de Mathématiques Pures et Appliquées 150, 24–63, 2021.

13. X. Liang, L. Zhang, The optimal distribution of resources and rate of migration maximizing the

population size in logistic model with identical migration, Discrete & Continuous Dynamical

Systems-Series B 26(4), 2021.

14. X. Liang, T. Zhou, Spreading speeds of nonlocal KPP equations in almost periodic media,

Journal of Functional Analysis 279(9), 108723, 2020.

15. X. Liang, T. Zhou, Spreading speeds of KPP-type lattice systems in heterogeneous media,

Communications in Contemporary Mathematics 22(01), 1850083, 2020.

16. X. Liang, T. Zhou, Transition semi-wave solutions of reaction diffusion equations with free

boundaries, Journal of Differential Equations 267(10), 5601–5630, 2019.

17. X. Liang, L. Zhang, X.-Q. Zhao, Basic reproduction ratios for periodic abstract functional

differential equations with application to a spatial model for Lyme disease, Journal of Dynamics

and Differential Equations 31(3), 1247–1278, 2019.

18. W. Ding, Y. Du, X. Liang, Spreading in space–time periodic media governed by a monostable

equation with free boundaries, Part 2: Spreading speed, Annales de l’Institut Henri Poincaré

C, Analyse non linéaire 36(6), 1539–1573, 2019.10 

19. X. Liang, L. Zhang, X.-Q. Zhao, The principal eigenvalue for periodic nonlocal dispersal

systems with time delay, Journal of Differential Equations 266(4), 2100–2124, 2019.

20. X. Liang, Semi-Wave Solutions of KPP-Fisher Equations with Free Boundaries in Spatially

Almost Periodic Media, Journal de Mathématiques Pures et Appliquées, 2018.

21. W. Ding, Y. Du, X. Liang, Spreading in space–time periodic media governed by a monostable

equation with free boundaries, Part 1: Continuous initial functions, Journal of Differential

Equations 262(10), 4988–5021, 2017.

22. X. Liang, L. Zhang, X.-Q. Zhao, The principal eigenvalue for degenerate periodic reaction-

diffusion systems, SIAM Journal on Mathematical Analysis 49(5), 3603–3636, 2017.

23. F. Li, X. Liang, W. Shen, Diffusive KPP equations with free boundaries in time almost periodic

environments: II. Spreading speeds and semi-wave solutions, Journal of Differential Equations

261(4), 2403–2445, 2016.

24. F. Li, X. Liang, W. Shen, Diffusive KPP equations with free boundaries in time almost periodic

environments: I. Spreading and vanishing dichotomy, arXiv preprint arXiv:1507.01881, 2015.

25. Y. Du, X. Liang, Pulsating semi-waves in periodic media and spreading speed determined by

a free boundary model, Annales de l’Institut Henri Poincaré C, Analyse non linéaire 32(2),

279–305, 2015.

26. W. Ding, X. Liang, Principal eigenvalues of generalized convolution operators on the circle

and spreading speeds of noncompact evolution systems in periodic media, SIAM Journal on

Mathematical Analysis 47(1), 855–896, 2015.

27. X. Liang, H. Matano, Maximizing the spreading speed of KPP fronts in two-dimensional

stratified media, Proceedings of the London Mathematical Society 109(5), 1137–1174, 2014.

28. W. Ding, X. Liang, B. Xu, Spreading speeds of N-season spatially periodic integro-difference

models, Discrete and Continuous Dynamical Systems 33, 3443–3472, 2013.

29. J.-S. Guo, X. Liang, The minimal speed of traveling fronts for the Lotka–Volterra competition

system, Journal of Dynamics and Differential Equations 23(2), 353–363, 2011.

30. X. Liang, X. Lin, H. Matano, A variational problem associated with the minimal speed of trav-

elling waves for spatially periodic reaction-diffusion equations, Transactions of the American

Mathematical Society 362(11), 5605–5633, 2010.

31. X. Liang, X.-Q. Zhao, Spreading speeds and traveling waves for abstract monostable evolution

systems, Journal of Functional Analysis 259(4), 857–903, 2010.

32. X. Liang, X.-Q. Zhao, Erratum: Asymptotic speeds of spread and traveling waves for monotone

semiflows with applications, Communications on Pure and Applied Mathematics, 2008.

33. Y. Du, X. Liang, A diffusive competition model with a protection zone, Journal of Differential

Equations 244(1), 61–86, 2008.10 

34. D. Gao, X. Liang, A competition-diffusion system with a refuge, Discrete and Continuous

Dynamical Systems Series B 8(2), 435, 2007.

35. X. Liang, X.-Q. Zhao, Asymptotic speeds of spread and traveling waves for monotone semiflows

with applications, Communications on Pure and Applied Mathematics, 2007.

36. X. Liang, Y. Yi, X.-Q. Zhao, Spreading speeds and traveling waves for periodic evolution

systems, Journal of Differential Equations 231(1), 57–77, 2006.

37. J. Jiang, X. Liang, Competitive systems with migration and the Poincaré-Bendixson theorem

for a 4-dimensional case, Quarterly of Applied Mathematics 64(3), 483–498, 2006.

38. J. Jiang, X. Liang, X.-Q. Zhao, Saddle-point behavior for monotone semiflows and reaction–

diffusion models, Journal of Differential Equations 203(2), 313–330, 2004.

39. X. Liang, J. Jiang, The dynamical behaviour of type-K competitive Kolmogorov systems and

its application to three-dimensional type-K competitive Lotka–Volterra systems, Nonlinearity

16(3), 785–801, 2003.

40. X. Liang, J. Jiang, Discrete infinite-dimensional type-K monotone dynamical systems and

time-periodic reaction–diffusion systems, Journal of Differential Equations 189(1), 318–354,

2003.

41. X. Liang, J. Jiang, The classification of the dynamical behavior of 3-dimensional type K mono-

tone Lotka–Volterra systems, Nonlinear Analysis: Theory, Methods & Applications 51(5),

749–763, 2002.

42. X. Liang, J. Jiang, On the topological entropy, nonwandering set and chaos of monotone and

competitive dynamical systems, Chaos, Solitons & Fractals 14(5), 689–696, 2002.

43. X. Liang, J. Jiang, On the finite-dimensional dynamical systems with limited competition,

Transactions of the American Mathematical Society 354(9), 3535–3554, 2002.