126 citations · 158 across the 17 of their papers we have counts for
12 papers · 1 filter
Global Dynamics of Nonlocal Diffusion Systems on Time-Varying Domains
Xiandong Lin, Hailong Ye, Xiao-Qiang Zhao
We propose a class of nonlocal diffusion systems on time-varying domains, and fully characterize their asymptotic dynamics in the asymptotically fixed, time-periodic and unbounded…
Asymptotic behavior of the basic reproduction ratio for periodic reaction-diffusion systems
Lei Zhang, Xiao-Qiang Zhao
This paper is devoted to the study of asymptotic behavior of the basic reproduction ratio for periodic reaction-diffusion systems in the case of small and large diffusion coefficie…
Propagation Dynamics for Monotone Evolution Systems without Spatial Translation Invariance
Taishan Yi, Xiao-Qiang Zhao
In this paper,under an abstract setting we establish the existence of spatially inhomogeneous steady states and the asymptotic propagation properties for a large class of monotone…
Propagation dynamics of a reaction-diffusion equation in a time-periodic shifting environment
Jian Fang, Rui Peng, Xiao-Qiang Zhao
This paper concerns the nonautonomous reaction-diffusion equation \[ u_t=u_{xx}+ug(t,x-ct,u), \quad t>0,x\in\mathbb{R}, \] where is the shifting speed, and the tim…
Notes on nonlocal dispersal equations in a periodic habitat
Jian Fang, Xiao-Qiang Zhao
In this paper, we prove that the solution maps of a large class of nonlocal dispersal equations are -contractions, where is the Kuratowski measure of noncompactness. Then we…
Spatial Dynamics of a Nonlocal Dispersal Population Model in a Shifting Environment
Wan-Tong Li, Jia-Bing Wang, Xiao-Qiang Zhao
This paper is concerned with spatial spreading dynamics of a nonlocal dispersal population model in a shifting environment where the favorable region is shrinking. It is shown that…
Notes on solution maps of abstract FDEs
Xiao-Qiang Zhao
It is shown that the solution maps of an abstract functional differential equations (FDEs) are -contractions in the phase space equipped with an equivalent norm under appropriat…
Traveling waves and spreading speeds for time-space periodic monotone systems
Jian Fang, Xiao Yu, Xiao-Qiang Zhao
The theory of traveling waves and spreading speeds is developed for time-space periodic monotone semiflows with monostable structure. By using traveling waves of the associated Poi…
Propagation Phenomena for A Reaction-Advection-Diffusion Competition Model in A Periodic Habitat
Xiao Yu, Xiao-Qiang Zhao
This paper is devoted to the study of propagation phenomena for a Lotka-Volterra reaction-advection-diffusion competition model in a periodic habitat. We first investigate the glob…
Bistable pulsating fronts for reaction-diffusion equations in a periodic habitat
Weiwei Ding, Francois Hamel, Xiao-Qiang Zhao
This paper is concerned with the existence and qualitative properties of pulsating fronts for spatially periodic reaction-diffusion equations with bistable nonlinearities. We focus…
Exponential and Algebraical Stability of Traveling Wavefronts in Periodic Spatial-Temporal Environments
Ming Mei, Chunhua Ou, Xiao-Qiang Zhao
Global stability of traveling wavefronts in a periodic spatial-temporal environment in -dimension () is studied. The wavefront is proved to be exponentially stable in th…
Bistable Traveling Waves for Monotone Semiflows with Applications
Jian Fang, Xiao-Qiang Zhao
This paper is devoted to the study of traveling waves for monotone evolution systems of bistable type. Under an abstract setting, we establish the existence of bistable traveling w…