The current paper is devoted to the study of spatial spreading dynamics of monostable
equations with nonlocal dispersal in spatially periodic habitats. In particular, the existence …

In this paper, we introduce a generalization of travelling waves for evolution equations. We
are especially interested in reaction-diffusion equations and systems in heterogeneous …

In this paper, we generalize the usual notions of waves, fronts, and propagation speeds in a
very general setting. These new notions, which cover all usual situations, involve uniform …

This paper is concerned with the existence of pulsating traveling fronts for the equation:
where the diffusion matrix A, the advection term q and the reaction term f are periodic in t …

We study the existence, uniqueness, and asymptotic stability of time periodic traveling wave
solutions to a periodic diffusive Lotka–Volterra competition system. Under certain conditions …

In this paper, we first establish the existence of traveling waves and spreading speeds for
time–space periodic monotone systems with monostable structure via the Poincaré maps …

In this paper, we prove various qualitative properties of pulsating traveling fronts in periodic
media, for reaction-diffusion equations with Kolmogorov–Petrovsky–Piskunov type or …

We prove the uniqueness, up to shifts, of pulsating traveling fronts for reaction-diffusion
equations in periodic media with Kolmogorov–Petrovskiĭ–Piskunov type nonlinearities …

In the current paper, we consider the following parabolic–elliptic semilinear Keller–Segel
model on RN,{ut=∇⋅(∇ u− χ u∇ v)+ au− bu 2, x∈ RN, t> 0, 0=(Δ− I) v+ u, x∈ RN, t> 0 …

We prove the existence of Kolmogorov-Petrovsky-Piskunov (KPP) type traveling fronts in
space-time periodic and mean zero incompressible advection, and establish a variational …