Open AccessRecent developments on spatial propagation for diffusion equations in shifting environments
Author(s) -
Jiabing Wang,
Wan–Tong Li,
Fang-Di Dong,
Shao-Xia Qiao
Publication year - 2022
Publication title -
discrete and continuous dynamical systems. series b
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.864
H-Index - 53
eISSN - 1553-524X
pISSN - 1531-3492
DOI - 10.3934/dcdsb.2021266
Subject(s) - biological dispersal , reaction–diffusion system , diffusion , partial differential equation , competition (biology) , lattice (music) , computer science , statistical physics , mathematics , ecology , physics , mathematical analysis , sociology , biology , demography , population , acoustics , thermodynamics
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.