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We study the propagation speed of bistable traveling waves in the classical two-component diffusive Lotka-Volterra system under strong competition. From an ecological perspective, the sign of the propagation speed determines the long-term…

Analysis of PDEs · Mathematics 2025-10-17 Ken-Ichi Nakamura , Toshiko Ogiwara

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

In this article we investigate two free boundary problems for a Lotka-Volterra competition system in a higher space dimension with sign-changing coefficients. One may be viewed as describing how two competing species invade if they occupy…

Analysis of PDEs · Mathematics 2015-04-13 Yonggang Zhao , Mingxin Wang

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…

Dynamical Systems · Mathematics 2015-12-01 Liang Kong , Nar Rawal , Wenxian Shen

This article is concerned with a system of semilinear parabolic equations with two free boundaries describing the spreading fronts of the invasive species in a mutualistic ecological model. The local existence and uniqueness of a classical…

Analysis of PDEs · Mathematics 2014-05-20 Mei Li

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 Souganidis, to establish upper and lower estimates of…

Analysis of PDEs · Mathematics 2021-01-19 King-Yeung Lam , Qian Liu , Shuang Liu

In this paper, we shall establish the spreading speed and existence of traveling waves for a non-cooperative system arising from epidermal wound healing and characterize the spreading speed as the slowest speed of a family of non-constant…

Quantitative Methods · Quantitative Biology 2010-07-09 Haiyan Wang

This short paper concerns a diffusive logistic equation with the heterogeneous environment and a free boundary, which is formulated to study the spread of an invasive species, where the free boundary represents the expanding front. A…

Analysis of PDEs · Mathematics 2014-06-25 Mingxin Wang

This paper concerns the spreading speed and asymptotical behaviors, which was left as an open problem in \cite{LLW22}, of a Fisher-KPP nonlocal diffusion model with a free boundary. Using a new lower solution, we get the exact finite…

Analysis of PDEs · Mathematics 2024-09-25 Lei Li , Mingxin Wang

In this paper, we study the propagation dynamics for a class of integrodifference competition models in a periodic habitat. An interesting feature of such a system is that multiple spreading speeds can be observed, which biologically means…

Dynamical Systems · Mathematics 2017-12-22 Ruiwen Wu , Xiao-Qiang Zhao

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

In this paper, we consider the diffusive competition problem consisting of an invasive species with density $u$ and a native species with density $v$. We assume that $v$ undergoes diffusion and growth in $[0, \infty)$, and $u$ exists…

Analysis of PDEs · Mathematics 2015-04-22 Qiaoling Chen , Fengquan Li , Feng Wang

In this paper we investigate some free boundary problems for the Lotka-Volterra type prey-predator model in one space dimension. The main objective is to understand the asymptotic behavior of the two species (prey and predator) spreading…

Analysis of PDEs · Mathematics 2014-01-14 Mingxin Wang

This paper investigates the large time behaviour of a three species reaction-diffusion system, modelling the spatial invasion of two predators feeding on a single prey species. In addition to the competition for food, the two predators…

Analysis of PDEs · Mathematics 2020-07-07 Arnaud Ducrot , Thomas Giletti , Jong-Shenq Guo , Masahiko Shimojo

This paper is concerned with the asymptotic spreading behavior of solutions of the Lotka-Volterra system with strong competition in $\mathbb{R}^{N}$. Two types of initial conditions are proposed: (C1) two species initially occupy bounded…

Analysis of PDEs · Mathematics 2024-11-22 Hui Bao , Hongjun Guo

In this paper, we mainly investigate the spreading dynamics of a nonlocal diffusion KPP model with free boundaries which is firstly explored in time almost periodic media. As the spreading occurs, the long-run dynamics are obtained.…

Analysis of PDEs · Mathematics 2023-09-18 Chengcheng Cheng , Rong Yuan

This paper is concerned with the limit, as the interspecific competition rate goes to infinity, of pulsating front solutions in space-periodic media for a bistable two-species competition--diffusion Lotka--Volterra system. We distinguish…

Analysis of PDEs · Mathematics 2017-12-15 Léo Girardin , Grégoire Nadin

The theory of traveling waves and spreading speeds is developed for time-space periodic monotone semiflows with monostable structure. By using traveling waves of the associated Poincar\'e maps in a strong sense, we establish the existence…

Analysis of PDEs · Mathematics 2015-04-16 Jian Fang , Xiao Yu , Xiao-Qiang Zhao

Spiral waves are a ubiquitous feature of the nonequilibrium dynamics of a great variety of excitable systems. In the limit of a large separation in timescale between fast excitation and slow recovery, one can reduce the spiral problem to…

patt-sol · Physics 2009-10-30 David A. Kessler , Herbert Levine

We consider a family of controlled reaction-diffusion equations, describing the spatial spreading of an invasive biological species. For a given propagation speed $c\in{I\!\!R}$, we seek a control with minimum cost, which achieves a…

Optimization and Control · Mathematics 2023-02-21 Alberto Bressan , Minyan Zhang