Related papers: The diffusive competition problem with a free boun…
Frequency-dependent selection reflects the interaction between different species as they battle for limited resources in their environment. In a stochastic evolutionary game the species relative fitnesses guides the evolutionary dynamics…
In this paper, we study the dynamics of the ratio-dependent type prey-predator model with different free boundaries. The two free boundaries, determined by prey and predator respectively, implying that they may intersect each other as time…
In this paper, we study a competitive model involving two species. When the competition is strong enough, the two species are separated by a free boundary. If the initial data has a positive bound at infinity. We prove that the solution…
A mutualist model with nonlocal diffusions and a free boundary is first considered. We prove that this problem has a unique solution defined $t\ge0$, and its dynamics are governed by a spreading-vanishing dichotomy. Some criteria for…
This is part II of our study on the free boundary problems with nonlocal and local diffusions. In part I, we obtained the existence, uniqueness, regularity and estimates of global solution. In part II here, we show a spreading-vanishing…
We study nonlinear diffusion problems of the form $u_t=u_{xx}+f(u)$ with free boundaries. Such problems may be used to describe the spreading of a biological or chemical species, with the free boundary representing the expanding front. For…
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 decaying in a right half-line. Thanks to a careful…
This is the first of two papers where we discuss the limits imposed by competition to the biodiversity of species communities. In this first paper we study the coexistence of competing species at the fixed point of population dynamic…
We investigate the controllability of the competition-diffusion Lotka-Volterra system. Our primary focus is on the one-dimensional setting with Dirichlet boundary controls, interpreted as ecological management policies regulating the…
For two resource-sharing species we explore the interplay of harvesting and dispersal strategies, as well as their influence on competition outcomes. Although the extinction of either species can be achieved by excessive culling, choosing a…
The current paper is concerned with the existence of spreading speeds and linear determinacy for two species competition systems with nonlocal dispersal in time and space periodic habitats. The notion of spreading speed intervals for such a…
Species introductions to new habitats can cause a decline in the population size of competing native species and consequently also in their genetic diversity. We are interested in why these adverse effects are weak in some cases whereas in…
We consider the classical two-species Lotka-Volterra competition-diffusion system in the strong-weak competition case. When the corresponding minimal speed of the traveling waves is not linear determined, we establish the precise asymptotic…
We study a diffusive Lotka-Volterra competition system with advection under Neumann boundary conditions. Our system models a competition relationship that one species escape from the region of high population density of their competitors in…
This paper concerns the sharp asymptotic profiles of the solution of a diffusive epidemic model with one free boundary and one fixed boundary which is subject to the homogeneous Dirichlet boundary condition and Neumann boundary condition,…
Habitat fragmentation, often driven by human activities, alters ecological landscapes by disrupting connectivity and reshaping species interactions. In such fragmented environments, habitats can be modeled as networks, where individuals…
In this paper, we first consider two scalar nonlocal diffusion problems with a free boundary and a fixed boundary. We obtain the global existence, uniqueness and longtime behaviour of solution of these two problems. The spreading-vanishing…
Invasion fronts in ecology are well studied but very few mathematical results concern the case with variable motility (possibly due to mutations). Based on an apparently simple reaction-diffusion equation, we explain the observed phenomena…
Both community ecology and conservation biology seek further understanding of factors governing the advance of an invasive species. We model biological invasion as an individual-based, stochastic process on a two-dimensional landscape. An…
We study free boundary problem of Fisher-KPP equation $u_t=u_{xx}+u(1-u),\ t>0,\ ct<x<h(t)$. The number $c>0$ is a given constant, $h(t)$ is a free boundary which is determined by the Stefan-like condition. This model may be used to…