On spatial-temporal dynamics of a Fisher-KPP equation with a shifting environment

By Haijun Hu, Taishan Yi, Xingfu Zou. Proceedings of the American Mathematical Society, 2019

102 citations recorded by the source corpus.

We consider a generalized Fisher-KPP equation with the growth function being time and space dependent in the form of “shifting with constant speed”. The main concerns are extinction and persistence, as well as spatial-temporal dynamics. By employing a new method relating to semigroup and some subtle estimates, we not only extend the main results in Li et al. [SIAM J. Appl. Math. 74 (2014), pp. 1397-1417] to a scenario when the growth function may have no sign change, but also improve the main results there by dropping some restrictions on the initial functions.

Subfields: Modeling and Simulation, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/53acc967c31c8b6a79772e0be0fb56383b41be24

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In Modeling and Simulation

1. Taishan Yi
2. Xiao-Qiang Zhao
3. Xingfu Zou
4. Chufen Wu
5. Yang Wang
6. Jianhong Wu
7. Wan-Tong Li
8. Guo Lin

In Public Health, Environmental and Occupational Health

1. Taishan Yi
2. Xiao-Qiang Zhao
3. Xingfu Zou
4. Chufen Wu
5. Yang Wang
6. Wan-Tong Li
7. Guo Lin
8. Shigui Ruan

Citations in the corpus

• Stability of Almost Periodic Nicholson’s Blowflies Model Involving Patch Structure and Mortality Terms (2019, unknown): “1 Introduction The qualitative theory of differential equations model has been an attractive topic because of its significance and applications in areas such as physics, mathematical biology, and control theory [9,11,21,26].”
• Spatial-temporal dynamics of a Lotka-Volterra competition model with nonlocal dispersal under shifting environment (2019, background): “[23] investigated the spatial-temporal dynamics of (1) under the critical no-sign-change situation for the growth function: 0 ≤ r(−∞) < r(∞).”
• Propagation dynamics for monotone evolution systems without spatial translation invariance (2020, background): “1-(i-iii) was established in [19] in the case where lim s→−∞ r(s) = 0 and c > 0.”