61 citations · 211 across the 15 of their papers we have counts for
16 papers
A Hamilton-Jacobi Approach to Time-Delayed Nonlocal Diffusion Models in Shifting Habitats
Bing-Er Jiang, King-Yeung Lam, Wan-Tong Li +1
This paper is concerned with the spatial propagation dynamics of time-delayed nonlocal diffusion equations in shifting habitats. We employ the theory of viscosity solutions for Ham…
A Hamilton-Jacobi Approach to Evolution of Dispersal
King-Yeung Lam, Yuan Lou, Benoit Perthame
The evolution of dispersal is a classical question in evolutionary biology, and it has been studied in a wide range of mathematical models. A selection-mutation model, in which the…
Niche differentiation in the light spectrum promotes coexistence of phytoplankton species: a spatial modelling approach
Christopher M. Heggerud, King-Yeung Lam, Hao Wang
The paradox of the plankton highlights the apparent contradiction between Gause's law of competitive exclusion and the observed diversity of phytoplankton. It is well known that ph…
Asymptotic spreading of KPP reactive fronts in heterogeneous shifting environments
King-Yeung Lam, Xiao Yu
We study the asymptotic spreading of Kolmogorov-Petrovsky-Piskunov (KPP) fronts in heterogeneous shifting habitats, with any number of shifting speeds, by further developing the me…
On the evolution of slow dispersal in multi-species communities
Robert Stephen Cantrell, King-Yeung Lam
For any , we show that there are choices of diffusion rates such that for competing species which are ecologically identical and having distinct dif…
Ideal Free Dispersal under General Spatial heterogeneity and Time Periodicity
Robert Stephen Cantrell, Chris Cosner, King-Yeung Lam
A population is said to have an ideal free distribution in a spatially heterogeneous but temporally constant environment if each of its members have chosen a fixed spatial location…
Selected topics on reaction-diffusion-advection models from spatial ecology
King-Yeung Lam, Shuang Liu, Yuan Lou
We discuss the effects of movement and spatial heterogeneity on population dynamics via reaction-diffusion-advection models, focusing on the persistence, competition, and evolution…
Entire Solutions of Diffusive Lotka-Volterra System
King-Yeung Lam, Rachidi B. Salako, Qiliang Wu
This work is concerned with the existence of entire solutions of the diffusive Lotka-Volterra competition system \begin{equation}\label{eq:abstract} \begin{cases} u_{t}= u_{xx} + u…
Stacked invasion waves in a competition-diffusion model with three species
King-Yeung Lam, Qian Liu, Shuang Liu
We investigate the spreading properties of a three-species competition-diffusion system, which is non-cooperative. We apply the Hamilton-Jacobi approach, due to Freidlin, Evans and…
Asymptotic spreading of interacting species with multiple fronts I: A geometric optics approach
Qian Liu, Shuang Liu, King-Yeung Lam
We establish spreading properties of the Lotka-Volterra competition-diffusion system. When the initial data vanish on a right half-line, we derive the exact spreading speeds and pr…
Asymptotic spreading of interacting species with multiple fronts II: Exponentially decaying initial data
Qian Liu, Shuang Liu, King-Yeung Lam
This is part two of our study on the spreading properties of the Lotka-Volterra competition-diffusion systems with a stable coexistence state. We focus on the case when the initial…
Uniqueness of the viscosity solution of a constrained Hamilton-Jacobi equation
Vincent Calvez, King-Yeung Lam
In quantitative genetics, viscosity solutions of Hamilton-Jacobi equations appear naturally in the asymptotic limit of selection-mutation models when the population variance vanish…
Two-locus clines maintained by diffusion and recombination in a heterogeneous environment
Linlin Su, King-Yeung Lam, Reinhard Bürger
We study existence and stability of stationary solutions of a system of semilinear parabolic partial differential equations that occurs in population genetics. It describes the evo…
Invasion of open space by two competitors: spreading properties of monostable two-species competition--diffusion systems
Léo Girardin, King-Yeung Lam
This paper is concerned with some spreading properties of monostable Lotka--Volterra two-species competition--diffusion systems when the initial values are null or exponentially de…
A mutation-selection model for evolution of random dispersal
King-Yeung Lam, Yuan Lou
We consider a mutation-selection model of a population structured by the spatial variables and a trait variable which is the diffusion rate. Competition for resource is local in sp…
Concentration Phenomena of a Semilinear Elliptic Equation with Large Advection in an Ecological Model
King-Yeung Lam
We consider a reaction-diffusion-advection equation arising from a biological model of migrating species. The qualitative properties of the globally attracting solution are studied…