English
Related papers

Related papers: Free boundary problems for a Lotka-Volterra compet…

200 papers

The current series of research papers is to investigate the asymptotic dynamics in logistic type chemotaxis models in one space dimension with a free boundary or unbounded boundary. Such a model with a free boundary describes the spreading…

Dynamical Systems · Mathematics 2020-02-11 Lianzhang Bao , 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 characterize the spreading of a new species in time almost…

Dynamical Systems · Mathematics 2015-07-08 Fang Li , Xing Liang , Wenxian Shen

In this paper, we study three two competing species Lotka-Volterra competition models on finite connected graphs, with Dirichlet, Neumann or no boundary conditions. We get that when time goes to infinity, either one specie extincts while…

Analysis of PDEs · Mathematics 2022-10-26 Yuanyang Hu , Chengxia Lei

In this work, we investigate the long-time dynamics of a two species competition model of Lotka-Volterra type with nonlocal diffusions. One of the species, with density $v(t,x)$, is assumed to be a native in the environment (represented by…

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

This paper studies the spreading dynamics of a high-dimensional strong competition Lotka-Volterra system where two species initially occupy disjoint measurable (possibly unbounded) subsets in $\mathbb{R}^N$, which are called initial…

Analysis of PDEs · Mathematics 2026-02-26 Hongjun Guo

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…

Analysis of PDEs · Mathematics 2021-10-28 Lei Li , Mingxin Wang

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…

Analysis of PDEs · Mathematics 2019-06-19 Léo Girardin , King-Yeung Lam

This paper investigates the dynamics of a reaction-diffusion system with two free boundaries, modeling the invasion of two cooperative species, where the free boundaries represent expanding fronts. We first analyze the long-term behavior of…

Analysis of PDEs · Mathematics 2025-11-21 Qian Qin , JinJing Jiao , Zhiguo Wang , Hua Nie

We investigate the long term behavior for a class of competition-diffusion systems of Lotka-Volterra type for two competing species in the case of low regularity assumptions on the data. Due to the coupling that we consider the system…

Analysis of PDEs · Mathematics 2008-06-06 Marco Squassina

In this paper, we consider a Leslie-Gower predator-prey model in one-dimensional environment. We study the asymptotic behavior of two species evolving in a domain with a free boundary. Sufficient conditions for spreading success and…

Analysis of PDEs · Mathematics 2018-12-03 Yunfeng Liu , Zhiming Guo , Mohammad El Smaily , Lin Wang

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

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 describe the spreading of a new or invasive species, with the free…

Analysis of PDEs · Mathematics 2016-11-08 Weiwei Ding , Yihong Du , Xing Liang

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

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

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

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 consider the diffusive competition problem with a free boundary and sign-changing intrinsic growth rate in heterogeneous time-periodic environment, consisting of an invasive species with density $u$ and a native species…

Analysis of PDEs · Mathematics 2015-04-24 Qiaoling Chen , Fengquan Li , Feng Wang

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

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

This paper involves a diffusive epidemic model whose domain has one free boundary with the Stefan boundary condition, and one fixed boundary subject to the usual homogeneous Dirichlet or Neumann condition. By using the standard upper and…

Analysis of PDEs · Mathematics 2024-05-03 Xueping Li , Lei Li , Ying Xu , DanDan Zhu