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

We consider a competitive system with nonlocal dispersals in a 1-dimensional environment
that is worsening with a constant speed, reflected by two shifting growth functions. By …

This paper is concerned with the propagation dynamics of the time periodic Lotka-Volterra
competition systems with nonlocal dispersal in a shifting habitat. We first obtain three types …

This paper deals with the propagation dynamics for lattice differential equations in a time-
periodic shifting habitat. We prove the existence, uniqueness and global exponential …

This paper is concerned with the asymptotic propagations for a nonlocal dispersal
population model with shifting habitats. In particular, we verify that the invading speed of the …

This paper is concerned with parabolic gradient systems of the form\[u_t=-\nabla V (u)+ u_
{xx}\,,\] where the spatial domain is the whole real line, the state variable $ u $ is …

As the global climate changes, biological populations have to adapt in place or move in
space to stay within their preferred temperature regime. Empirical evidence suggests that …

We study the effect of directional quenching on patterns formed in simple bistable systems
such as the Allen–Cahn and the Cahn–Hilliard equation on the plane. We model directional …

This paper is concerned with parabolic gradient systems of the form\[u_t=-\nabla V
(u)+\Delta_x u\,,\] where the space variable $ x $ and the state variable $ u $ are …

This paper is concerned with radially symmetric solutions of systems of the form\[u_t=-\nabla
V (u)+\Delta_x u\] where space variable $ x $ and and state-parameter $ u $ are …