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In this paper we consider the diffusive competition model consisting of an invasive species with density $u$ and a native species with density $v$, in a radially symmetric setting with free boundary. We assume that $v$ undergoes diffusion…

Analysis of PDEs · Mathematics 2013-03-05 Yihong Du , Zhigui Lin

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…

Analysis of PDEs · Mathematics 2025-08-04 Elisa Affili , Enrique Zuazua

This paper concerns a diffusive logistic equation with a free boundary and sign-changing intrinsic growth rate in heterogeneous time-periodic environment, in which the variable intrinsic growth rate may be "very negative" in a "suitable…

Analysis of PDEs · Mathematics 2015-09-22 Mingxin Wang

This paper is concerned with the classical two-species Lotka-Volterra diffusion system with strong competition. The sharp dynamical behavior of the solution is established in two different situations: either one species is an invasive one…

Analysis of PDEs · Mathematics 2020-07-14 Rui Peng , Chang-Hong Wu , Maolin Zhou

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…

Analysis of PDEs · Mathematics 2015-05-28 Chunyi Gai , Qi Wang , Jingda Yan

This paper is concerned with the speeds of propagation for the monostable Lotka-Volterra competition-diffusion system in general unbounded domains of $\mathbb{R}^N$. We first establish various definitions of spreading speeds at large time…

Analysis of PDEs · Mathematics 2026-03-26 Yang-Yang Yan , Wei-Jie Sheng

We determine the asymptotic spreading speed of an invasive species, which invades the territory of a native competitor, governed by a diffusive competition model with a free boundary in a spherically symmetric setting. This free boundary…

Analysis of PDEs · Mathematics 2015-06-19 Yihong Du , Mingxin Wang , Maolin Zhou

We investigate the controllability of a generalized diffusive Lotka-Volterra competition model for two species, incorporating boundary controls and an interior multiplicative control. Considering a smooth, bounded N-dimensional domain, we…

Analysis of PDEs · Mathematics 2025-11-04 João Carlos Barreira , Maicon Sonego , Enrique Zuazua

Our interest here is to find the invader in a two species, diffusive and competitive Lotka-Volterra system in the particular case of travelling wave solutions. We investigate the role of diffusion in homogeneous domains. We might expect a…

Analysis of PDEs · Mathematics 2015-07-01 Léo Girardin , Grégoire Nadin

In this work we consider three species competing with each other in the same habitat. One of the species lives in the entire habitat, competing with the other two species, while the other two inhabit two disjoint regions of the habitat.…

Analysis of PDEs · Mathematics 2024-08-07 Pablo Álvarez-Caudevilla , Cristina Brändle , Mónica Molina-Becerra , Antonio Suárez

The possible control of competitive invasion by infection of the invader and multiplicative noise is studied. The basic model is the Lotka-Volterra competition system with emergent carrying capacities. Several stationary solutions of the…

Populations and Evolution · Quantitative Biology 2015-08-24 Ivo Siekmann , Horst Malchow

In this paper we investigate a free boundary problem for the diffusive Leslie-Gower prey-predator model with double free boundaries in one space dimension. This system models the expanding of an invasive or new predator species in which the…

Analysis of PDEs · Mathematics 2017-10-27 Mingxin Wang , Qianying Zhang

Defeat and success of the competitive invasion of a populated area is described with a standard Lotka-Volterra competition model. The resident is adapted to the heterogeneous living conditions, i.e., its motion is modelled as…

Populations and Evolution · Quantitative Biology 2017-10-12 Michael Bengfort , Ivo Siekmann , Horst Malchow

In this paper we consider a free boundary problem which models the spreading of an invasive species whose spreading is enhanced by the changing climate. We assume that the climate is shifting with speed c and obtain a complete…

Analysis of PDEs · Mathematics 2019-08-13 Yuanyang Hu , Xinan Hao , Xianfa Song , Yihong Du

This is a continuation of our work \cite{dns-part1} to investigate the long-time dynamics of a two species competition model of Lotka-Volterra type with nonlocal diffusions, where the territory (represented by the real line $\R$) of a…

Analysis of PDEs · Mathematics 2024-03-29 Yihong Du , Wenjie Ni , Linfei Shi

In this paper we study a free boundary problem for a ratio-dependent predator-prey system in one space dimension, with the free boundary only caused by the prey. The long time behaviors of solution are discussed. Then we establish a…

Analysis of PDEs · Mathematics 2021-05-12 Lingyu Liu

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…

Analysis of PDEs · Mathematics 2013-12-17 Jian Yang

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…

Analysis of PDEs · Mathematics 2021-05-28 Lei Li , Mingxin Wang

In this paper we study a ratio-dependent predator-prey model with a free boundary causing by both prey and predator over a one dimensional habitat. We study the long time behaviors of the two species and prove a spreading-vanishing…

Analysis of PDEs · Mathematics 2020-09-30 Lingyu Liu

In this paper, we study the dynamics of a two-species competition model with two different free boundaries in heterogeneous time-periodic environment, where the two species adopt a combination of random movement and advection upward or…

Analysis of PDEs · Mathematics 2015-11-26 Qiaoling Chen , Fengquan Li , Feng Wang