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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

This paper concerns the free boundary problem of an epidemic model. The spatial movements of the infectious agents and the infective humans are approximated by nonlocal diffusion operators. Especially, both the growth rate of the agents and…

Analysis of PDEs · Mathematics 2024-06-11 Xueping Li , Lei Li , Mingxin Wang

We introduce a stochastic individual model for the spatial behavior of an animal population of dispersive and competitive species, considering various kinds of biological effects, such as heterogeneity of environmental conditions, mutual…

Probability · Mathematics 2016-07-05 Joaquin Fontbona , Sylvie Méléard

In this paper, we examine the long-time dynamics of an epidemic model whose diffusion and reaction terms involve nonlocal effects described by suitable convolution operators.The spreading front of the disease is represented by the free…

Analysis of PDEs · Mathematics 2022-03-01 Rong Wang , Yihong Du

We investigate the spreading behavior of two invasive species modeled by a Lotka-Volterra diffusive competition system with two free boundaries in a spherically symmetric setting. We show that, for the weak-strong competition case, under…

Analysis of PDEs · Mathematics 2017-10-17 Yihong Du , Chang-Hong Wu

This paper investigates the long-time dynamics of a nonlocal epidemic model with free boundaries, where a pathogen with density $u(t,x)$ and the infected humans with density $v(t,x)$ evolve according to a reaction-diffusion system with…

Analysis of PDEs · Mathematics 2026-02-06 Yao Chen , Yihong Du , Wan-Tong Li , Rong Wang

The present paper is devoted to the investigation of the long time dynamics for a double free boundary system with nonlocal diffusions, which models the infectious diseases transmitted via digestive system such as fecal-oral diseases,…

Dynamical Systems · Mathematics 2021-06-10 Thanh-Hieu Nguyen , Hoang-Hung Vo

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

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 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 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

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

We model the growth, dispersal and mutation of two phenotypes of a species using reaction-diffusion equations, focusing on the biologically realistic case of small mutation rates. After verifying that the addition of a small linear mutation…

Analysis of PDEs · Mathematics 2017-09-19 Aled Morris , Luca Börger , Elaine Crooks

We investigate the traveling front solutions of a nonlocal Lotka Volterra system to illustrate the outcome of the competition between two species. The existence of the front solution is obtained through a new monotone iteration scheme, the…

Dynamical Systems · Mathematics 2013-06-24 Xiaojie hou , Biao Wang , Zhence Zhang

We introduce and analyze a nonlocal version of the one-phase Stefan problem in which, as in the classical model, the rate of growth of the volume of the liquid phase is proportional to the rate at which energy is lost through the…

Analysis of PDEs · Mathematics 2018-05-09 Carmen Cortázar , Fernando Quirós , Noemí Wolanski

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 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 investigate a Fisher-KPP nonlocal diffusion model incorporating the effect of advection and free boundaries, aiming to explore the propagation dynamics of the nonlocal diffusion-advection model. Considering the effects of…

Analysis of PDEs · Mathematics 2023-09-13 Chengcheng Cheng

In this paper, we propose and analyze a nonlocal cooperative reaction--diffusion system with free boundaries and drift terms, motivated by directional epidemic spread. Lacking a variational structure but requiring sharper regularity of…

Analysis of PDEs · Mathematics 2025-10-14 Soufiane Bentout , Hoang-Hung Vo