Zhongwei Shen

Research Interests

Publications

1. Mesoscopic and macroscopic entropy balance equations in a stochastic dynamics and its deterministic limit.
   Submitted. (with Hong Qian)
2. From habitat decline to collapse: a spatially explicit approach connecting habitat degradation to destruction.
   Submitted. (with Yurij Salmaniw and Hao Wang)
3. Stochastic stability of physical measures in conservative systems.
   Submitted. (with Weiwei Qi and Yingfei Yi)
4. Quasi-stationary distributions of absorbed singular diffusion processes in higher dimensions.
   Submitted. (with Alex Hening, Weiwei Qi and Yingfei Yi)
5. Population dynamics under demographic and environmental stochasticity.
   Ann. Appl. Probab., accepted. (with Alex Hening, Weiwei Qi and Yingfei Yi)
6. Large deviation principle for quasi-stationary distributions and multiscale dynamics of absorbed singular diffusions.
   Probab. Theory Related Fields, 188 (2024), no. 1-2, 667-728. (with Weiwei Qi and Yingfei Yi)
7. Concentration of quasi-stationary distributions for one-dimensional diffusions with applications.
   Ann. Inst. Henri Poincaré Probab. Stat., 60 (2), 874-903. (with Shirou Wang and Yingfei Yi)
8. Population dynamics under climate change: persistence criterion and effects of fluctuations.
   J. Math. Biol., 84, 30 (2022). (with Wenxian Shen, Shuwen Xue and Dun Zhou)
9. Global dynamics of a diffusive competition model with habitat degradation.
   J. Math. Biol., 84, 18 (2022). (with Yurij Salmaniw and Hao Wang)
10. Transient dynamics of absorbed singular diffusions.
    J. Dynam. Differential Equations, 34, 3089 - 3129 (2022). (with Min Ji, Weiwei Qi and Yingfei Yi)
    Special issue in memory of Professor Genevieve Raugel.
11. Convergence to periodic probability solutions in Fokker-Planck equations. Supplementary Materials
    SIAM J. Math. Anal. 53 (2021), no. 2, 1958-1992. (with Min Ji, Weiwei Qi and Yingfei Yi)
12. Towards mesoscopic ergodic theory.
    Science China Mathematics 63 (2020) no. 9, 1853-1876. (with Weiwei Qi, Shirou Wang and Yingfei Yi)
    Special issue in memory of Professor Shantao Liao.
13. Noise-vanishing concentration and limit behaviors of periodic probability solutions.
    Differential Integral Equations 33 (2020), no. 5-6, 273-322. (with Min Ji, Weiwei Qi and Yingfei Yi)
14. Existence of periodic probability solutions to Fokker-Planck equations with applications.
    J. Funct. Anal. 277 (2019) 108281. (with Min Ji, Weiwei Qi and Yingfei Yi)
15. Analysis of a diffusive SIR model with seasonality and nonlocal incidence.
    SIAM J. Appl. Math. 79 (2019), no. 6, 2218-2241. (with Zhen Jin, Zhuanzhuan Liu and Hao Wang)
16. Quantitative concentration of stationary measures.
    Physica D: Nonlinear Phenomena 399 (2019) 73-85. (with Min Ji and Yingfei Yi)
17. Integrodifference equations in the presence of climate change: persistence criterion, travelling waves and inside dynamics.
    J. Math. Biol. (2018) 77:1649-1687. (with Mark A. Lewis and Nathan G. Marculis)
    Special issue in memory of Professor Karl Peter Hadeler.
18. Nonlocal dispersal equations in time-periodic media: principal spectral theory, limiting properties and long-time dynamics.
    J. Differential Equations 267 (2019), 1423-1466. (with Hoang-Hung Vo)
19. Global dynamics of an infinite-dimensional epidemic model with nonlocal state structures.
    J. Differential Equations 265 (2018), 5262-5296. (with Michael Y. Li and Zhipeng Qiu)
20. Convergence to equilibrium in Fokker-Planck equations.
    J. Dynam. Differential Equations 31 (2019), 1591-1615. (with Min Ji and Yingfei Yi)
    Special issue in memory of Professor George R. Sell.
21. Spreading speeds and traveling waves for space-time periodic nonlocal dispersal cooperative systems.
    Commun. Pure Appl. Anal. 2019, 18 (1) : 361-396. (with Xiongxiong Bao and Wenxian Shen)
22. Existence, uniqueness and stability of transition fronts of nonlocal equations in time heterogeneous bistable media.
    European J. Appl. Math. 31 (2020) no. 4, 601-645. (with Wenxian Shen)
23. Transition fronts in nonlocal Fisher-KPP equations in time heterogeneous media.
    Commun. Pure Appl. Anal. 15 (2016), No. 4, 1193-1213. (with Wenxian Shen)
24. Regularity of transition fronts in nonlocal dispersal evolution equations.
    J. Dynam. Differential Equations, 29 (2017), no. 3, 1071-1102. (with Wenxian Shen)
25. Regularity and stability of transition fronts in nonlocal equations with time heterogeneous ignition nonlinearity.
    J. Differential Equations 262 (2017), no.5, 3390-3430. (with Wenxian Shen)
26. Transition fronts in nonlocal equations with time heterogeneous ignition nonlinearity.
    Discrete Contin. Dyn. Syst. A, 37 (2017), no. 2, 1013-1037. (with Wenxian Shen)
    Special issue in memory of Professor Paul Fife.
27. Stability, uniqueness and recurrence of generalized traveling waves in time heterogeneous media of ignition type.
    Trans. Amer. Math. Soc. 369 (2017), no. 4, 2573-2613. (with Wenxian Shen)
28. Transition fronts in time heterogeneous and random media of ignition type.
    J. Differential Equations, 262 (2017), no.1, 454-485. (with Wenxian Shen)
29. Completeness for sparse potential scattering.
    J. Math. Phys., 55, 012108 (2014).
30. Lifshitz tails for Anderson models with sign-indefinite single-site potentials.
    Math. Nachr., 288 (2015), No.13, 1538-1563.
31. Existence, uniqueness and anisotropic-decay-caused Lifshitz tails of the integrated density of surface states for random surface models.
    Random Oper. Stoch. Equ., 22 (2014), no.4, 241-268.
32. An improved Combes-Thomas estimate of magnetic Schrodinger operators.
    Ark. Mat., 52 (2014), no. 2, 383-414.
33. Asymptotic dynamics of a class of coupled oscillators driven by white noises.
    Stoch. Dyn., 13 (2013), no. 4, 1350002. (with Wenxian Shen and Shengfan Zhou)
34. Synchronization of coupled stochastic systems with multiplicative noise.
    Stoch. Dyn., 10 (2010), no.3, 407-428. (with Shengfan Zhou and Xiaoying Han)
35. One-dimensional random attractor and rotation number of the stochastic damped sine-Gordon equation.
    J. Differential Equations, 248 (2010), no.6, 1432-1457. (with Shengfan Zhou and Wenxian Shen)