Xing Liang CV.pdf

Liang Xing

Professor and Ph.D. Supervisor

School of Mathematical Sciences, University of Science and Technology of China (USTC)

Education & Career

I entered the Department of Mathematics at USTC in 1994 for my undergraduate studies and obtained my Ph.D. in Science in 2003. My research focuses on the dynamics of differential equations, with a particular emphasis on spatio-temporal dynamics of diffusion systems and their applications.

Research Contributions

In recent years, my collaborators and I have made significant advances in the propagation theory of diffusion systems and eigenvalue problems of operators:

1. Monostable Propagation Theory: I established a dynamical systems framework for monostable diffusion propagation problems, resolving several key open questions in the field. My work published in Communications on Pure and Applied Mathematics(CPAM) has become one of the most cited papers in the journal over the past two decades.

   
   

2. Principal Eigenvalue Theory: I developed the theory of principal eigenvalues for differential and integral operators, providing rigorous theoretical analysis and numerical algorithms. This theory is widely applied in the theoretical and numerical analysis of the Basic Reproduction Number (R0) in epidemiology.

3. Complex Media & Interdisciplinary Links: I investigated diffusion propagation in complex media, discovering anomalous propagation phenomena and establishing novel connections between reaction-diffusion equations and fields such as differential dynamical systems, ergodic theory, and the spectral theory of Schrödinger operators.

   
   

Academic Impact

My work has been published in leading journals including CPAM, Advances in Mathematics, Mathematische Annalen, Journal de Mathématiques Pures et Appliquées(JMPA), and SIAM Journal on Mathematical Analysis(SIMA). Notably, my contributions in CPAMand the Journal of Functional Analysis(JFA) are now considered foundational literature in the study of parabolic propagation systems, widely applied to specific partial differential equations (PDEs) as well as ecological and epidemiological models. Surprisingly, some of my fundamental results have attracted substantial interest and found applications beyond these areas, notably among scholars in control theory, optimization, and mathematical physics—including Alberto Bressan (an invited speaker at the International Congress of Mathematicians).

Current Research Interests

My current interests include propagation phenomena in non-standard diffusion systems and their connections to various mathematical disciplines. Specific topics include:

• Homogenazition, Spectra of asymmetric second-order elliptic operators in hyperbolic spaces and their relation to parabolic propagation.

  
  

• Propagation phenomena in Lévy flight-generated diffusion systems, traveling wave solutions, and the connection to invariant foliation theory in dynamical systems.

Publications

1. 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.

2. 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:2507.21870, 2025.

3. W. Ding, F. Hamel, X. Liang, Bistable pulsating fronts in slowly oscillating one-dimensional environments, Journal de Mathématiques Pures et Appliquées, 2025.

4. W. Ding, X. Li, X. Liang, Time-periodic traveling waves and propagating terraces for multistable equations with a fractional Laplacian: An abstract dynamical systems approach, Journal of Functional Analysis 288(2), 2025.

5. X. Liang, L. Zhang, M. Zhang, The influence of advection on the propagation phenomena of reactiondiffusion equations with KPP-bistable nonlinearity, arXiv:2408.03187, 2024.

6. 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.

7. 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.

8. 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.

9. 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.

10. X. Liang, T. Zhou, Spreading speeds of nonlocal KPP equations in heterogeneous media, Acta Mathematica Sinica, English Series 38(1), 161–178, 2022.

411. 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.

12. 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.（许世壁教授生日专刊）

13. X. Liang, T. Zhou, Spreading speeds of nonlocal KPP equations in almost periodic media, Journal of Functional Analysis 279(9), 108723, 2020.

14. X. Liang, T. Zhou, Spreading speeds of KPP-type lattice systems in heterogeneous media, Communications in Contemporary Mathematics 22(01), 1850083, 2020.

15. X. Liang, T. Zhou, Transition semi-wave solutions of reaction diffusion equations with free boundaries, Journal of Differential Equations 267(10), 5601–5630, 2019.

16. 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.

17. 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.

18. 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.

19. X. Liang, Semi-Wave Solutions of KPP-Fisher Equations with Free Boundaries in Spatially Almost Periodic Media, Journal de Mathématiques Pures et Appliquées, 2018.

20. 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.

21. 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.

22. 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.

23. F. Li, X. Liang, W. Shen, Diffusive KPP equations with free boundaries in time almost periodic environments: I. Spreading and vanishing dichotomy, arXiv:1507.01881, 2015.

24. 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.

25. 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.

26. 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.

27. 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.

28. 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.

29. X. Liang, X. Lin, H. Matano, A variational problem associated with the minimal speed of travelling waves for spatially periodic reaction-diffusion equations, Transactions of the American Mathematical Society 362(11), 5605–5633, 2010.

30. X. Liang, X.-Q. Zhao, Spreading speeds and traveling waves for abstract monostable evolution systems, Journal of Functional Analysis 259(4), 857–903, 2010.

31. 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.

32. Y. Du, X. Liang, A diffusive competition model with a protection zone, Journal of Differential Equations 244(1), 61–86, 2008.

33. D. Gao, X. Liang, A competition-diffusion system with a refuge, Discrete and Continuous Dynamical Systems Series B 8(2), 435, 2007.

34. X. Liang, X.-Q. Zhao, Asymptotic speeds of spread and traveling waves for monotone semiflows with applications, Communications on Pure and Applied Mathematics, 2007.

35. 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.

36. 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.

37. 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.

38. 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.

39. 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.

40. X. Liang, J. Jiang, The classification of the dynamical behavior of 3-dimensional type K monotone Lotka–Volterra systems, Nonlinear Analysis: Theory, Methods & Applications 51(5), 749–763, 2002.

41. 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.

42. X. Liang, J. Jiang, On the finite-dimensional dynamical systems with limited competition, Transactions of the American Mathematical Society 354(9), 3535–3554, 2002.