The theory of reaction–diffusion waves begins in the 1930s with the works in population
dynamics, combustion theory and chemical kinetics. At the present time, it is a well …

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

The trajectory of fractional calculus has undergone several periods of intensive
development, both in pure and applied sciences. During the last few decades fractional …

We consider a two-species competition model in a one-dimensional advective environment,
where individuals are exposed to unidirectional flow. The two species follow the same …

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 …

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 …

Most mathematical studies on expanding populations have focused on the rate of range
expansion of a population. However, the genetic consequences of population expansion …

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 …

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 …