15 citations · 25 across the 16 of their papers we have counts for
18 papers
Variational Principles and Rearrangement Inequalities for asymmetric Operators on Periodic Lattices
Xing Liang
In this paper, we establish variational formulas and a rearrangement inequality for principal eigenvalues of asymmetric second-order difference operators on periodic lattices. For…
On advective nonlocal operators: multiplicity of principal eigenpairs
Arnaud Ducrot, Quentin Griette, Xing Liang
We study the existence and multiplicity of principal eigenvalues and eigenfunctions for a periodically heterogeneous nonlocal dispersal model with advection. The operator we consid…
Spreading speeds for Fisher-KPP equations with slowly decaying initial data in an almost periodic setting
Xing Liang, Linfeng Xu, Tao Zhou
This paper investigates the long-times behavior of the Fisher-KPP equation with slowly decaying initial data in an almost periodic medium. We mainly focus on two classes of initial…
Generalized principal eigenvalues of elliptic operators and spreading speeds of Fisher-KPP equations in two-scale almost periodic media
Xing Liang, Linfeng Xu, Tao Zhou
This paper is concerned with the asymptotic behavior of the generalized principal eigenvalues of elliptic operators and spreading speeds of Fisher-KPP equations in two-scale almost…
The influence of advection on the propagation phenomena of reaction-diffusion equations with KPP-bistable nonlinearity
Xing Liang, Lei Zhang, Mingmin Zhang
This paper is devoted to propagation phenomena for a reaction-diffusion-advection equation in a one-dimensional heterogeneous environment, where heterogeneity is reflected by the n…
Bistable pulsating fronts in slowly oscillating environments *
Weiwei Ding, François Hamel, Xing Liang
We consider reaction-diffusion fronts in spatially periodic bistable media with large periods. Whereas the homogenization regime associated with small periods had been well studied…
Almost-periodic ground state of the non-self-adjoint Jacobi operator and its applications
Xing Liang, Honngze Wang, Qi Zhou
We study the ground states of the one-dimensional non-self-adjoint Jacobi operators in the almost periodic media by using the method of dynamical systems. We show the existence of…
Traveling fronts for Fisher-KPP lattice equations in almost periodic media
Xing Liang, Hongze Wang, Qi Zhou +1
This paper investigates the existence of almost periodic traveling fronts for Fisher-KPP lattice equations in one-dimensional almost periodic media. By the Lyapunov exponent of the…
Spreading speeds of KPP-type lattice systems in heterogeneous media
Xing Liang, Tao Zhou
In this paper, we investigate spreading properties of the solutions of the Kolmogorov-Petrovsky-Piskunov-type, (to be simple,KPP-type) lattice system \begin{equation}\label{firsteq…
Transition semi-wave solutions of reaction diffusion equations with free boundaries
Xing Liang, Tao Zhou
In this paper, we define the transition semi-wave solution of the following reaction diffusion equation with free boundaries \begin{equation}\label{0.1} \left\{ \begin{aligned} u_{…
Spreading speeds of nonlocal KPP equations in heterogeneous media
Xing Liang, Tao Zhou
In this paper, we prove the existence of the spreading speed of nonlocal KPP equations in two cases: 1. The media is almost periodic and the kernel of diffusion is continuous; 2. T…
Semi-Wave Solutions of KPP-Fisher Equations with Free Boundaries in Spatially Almost Periodic Media
Xing Liang
In this paper we prove the existence and uniqueness of the almost periodic semi- wave (traveling wave) solutions of KPP-Fisher equations with free boundaries in spatially almost pe…
Spreading in space-time periodic media governed by a monostable equation with free boundaries, Part 1: Continuous initial functions
Weiwei Ding, Yihong Du, Xing Liang
We aim to classify the long-time behavior of the solution to a free boundary problem with monostable reaction term in space-time periodic media. Such a model may be used to describ…
Spreading in space-time periodic media governed by a monostable equation with free boundaries, Part 2: Spreading speed
Weiwei Ding, Yihong Du, Xing Liang
This is Part 2 of our work aimed at classifying the long-time behavior of the solution to a free boundary problem with monostable reaction term in space-time periodic media. In Par…
Diffusive KPP Equations with Free Boundaries in Time Almost Periodic Environments: II. Spreading Speeds and Semi-Wave
Fang Li, Xing Liang, Wenxian Shen
In this series of papers, we investigate the spreading and vanishing dynamics of time almost periodic diffusive KPP equations with free boundaries. Such equations are used to chara…
Diffusive KPP Equations with Free Boundaries in Time Almost Periodic Environments: I. Spreading and Vanishing Dichotomy
Fang Li, Xing Liang, Wenxian Shen
In this series of papers, we investigate the spreading and vanishing dynamics of time almost periodic diffusive KPP equations with free boundaries. Such equations are used to chara…
A variational problem associated with the minimal speed of travelling waves for spatially periodic reaction-diffusion equations
Xing Liang, Xiaotao Lin, Hiroshi Matano
We consider the equation where is a nonnegative measure on that is periodic in In the case where is a smoot…
Maximizing the spreading speed of KPP fronts in two-dimensional stratified media
Xing Liang, Xiaotao Lin, Hiroshi Matano
We consider the equation , with monostable nonliearity, where is a nonnegative measure on that is periodic…