In this short review, we describe some recent developments on the spatial propagation for
diffusion problems in shifting environments, including single species models, competition …

This paper deals with the existence of traveling wave solutions of the Fisher equation with a
shifting habitat representing a transition to a devastating environment. By constructing a pair …

Predicting and managing species' responses to climate change is one of the most significant
challenges of our time. Tools are needed to address problems associated with novel climatic …

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 …

This paper concerns the equation (0.1) ut= ux x+ f (x− ct, u), x∈ R, where c≥ 0 is a forcing
speed and f:(s, u)∈ R× R+→ R is asymptotically of KPP type as s→−∞. We are interested in …

This paper is mainly concerned with the forced waves and gap formations for a Lotka–
Volterra competition model with nonlocal dispersal and shifting habitats. We first show that …

This paper is concerned with the spatial dynamics of a nonlocal dispersal population model
in a shifting environment where the favorable region is shrinking. It is shown that the species …

This paper is devoted to the study of the propagation dynamics of a nonlocal dispersal
Fisher-KPP equation in a time-periodic shifting habitat. We first show that this equation …

We consider the Fisher-KPP equation in a wavelike shifting environment for which the wave
profile of the environment is given by a monotonically decreasing function changing signs …

This paper deals with the uniqueness and global stability of forced extinction waves for the
nonlocal dispersal Fisher-KPP equation in a shifting environment where the favorable …