doi: 10.3934/dcdsb.2021266
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Recent developments on spatial propagation for diffusion equations in shifting environments

1. 

School of Mathematics and Physics, China University of Geosciences, Wuhan 430074, China

2. 

Center for Mathematical Sciences, China University of Geosciences, Wuhan 430074, China

3. 

School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, China

4. 

School of Mathematics, Hangzhou Normal University, Hangzhou 310036, China

* Corresponding author: Wan-Tong Li

Received  March 2021 Revised  September 2021 Early access November 2021

Fund Project: Wang was partially supported by NSF of China (11901543) and the Fundamental Research Funds for the Central Universities, China University of Geosciences (Wuhan) (CUGSX01). Li was partially supported by NSF of China (11731005). Dong was partially supported by NSF of China (12101171) and the Zhejiang Province Natural Science Foundation (Q22A015337)

In this short review, we describe some recent developments on the spatial propagation for diffusion problems in shifting environments, including single species models, competition/cooperative models and chemotaxis models submitted to classical reaction-diffusion equations (with or without free boundaries), integro-difference equations, lattice differential equations and nonlocal dispersal equations. The considered topics may typically come from modeling the threats associated with global climate change and the worsening of the environment resulting from industrialization which lead to the shifting or translating of the habitat ranges, and also arise indirectly in studying the pathophoresis as well as some multi-stage invasion processes. Some open problems and potential research directions are also presented.

Citation: Jia-Bing Wang, Wan-Tong Li, Fang-Di Dong, Shao-Xia Qiao. Recent developments on spatial propagation for diffusion equations in shifting environments. Discrete and Continuous Dynamical Systems - B, doi: 10.3934/dcdsb.2021266
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