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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

Reaction-diffusion equations are studied on bounded, time-periodic domains with zero Dirichlet boundary conditions. The long-time behaviour is shown to depend on the principal periodic eigenvalue of a transformed periodic-parabolic problem.…

Analysis of PDEs · Mathematics 2023-07-18 Jane Allwright

We address the question: Why may reaction-diffusion equations with hysteretic nonlinearities become ill-posed and how to amend this? To do so, we discretize the spatial variable and obtain a lattice dynamical system with a hysteretic…

Analysis of PDEs · Mathematics 2017-11-28 Pavel Gurevich , Sergey Tikhomirov

This paper is devoted to the study of propagation dynamics for a large class of non-monotone evolution systems. In two directions of the spatial variable, such a system has two limiting systems admitting the spatial translation invariance.…

Dynamical Systems · Mathematics 2023-10-23 Taishan Yi , Xiao-Qiang Zhao

We investigate spreading properties of solutions of a large class of two-component reaction-diffusion systems, including prey-predator systems as a special case. By spreading properties we mean the long time behaviour of solution fronts…

Analysis of PDEs · Mathematics 2019-07-08 Arnaud Ducrot , Thomas Giletti , Hiroshi Matano

We consider a two-species reaction-diffusion system in one space dimension that is derived from an epidemiological model in a spatially periodic environment with two types of pathogens: the wild type and the mutant. The system is of a…

Analysis of PDEs · Mathematics 2025-01-22 Quentin Griette , Hiroshi Matano

This paper is concerned with a model for the dynamics of a single species in a one-dimensional heterogeneous environment. The environment consists of two kinds of patches, which are periodically alternately arranged along the spatial axis.…

Analysis of PDEs · Mathematics 2024-07-04 François Hamel , Frithjof Lutscher , Mingmin Zhang

We treat a model of population dynamics in a periodic environment presenting a fast diffusion line. This phenomenon is modelled via a "road-field" system, which is a system of coupled reaction-diffusion equations set in domains of different…

Analysis of PDEs · Mathematics 2020-10-01 Elisa Affili

This paper is devoted to the study of propagation phenomena for a Lotka-Volterra reaction-advection-diffusion competition model in a periodic habitat. We first investigate the global attractivity of a semi-trival steady state for the…

Analysis of PDEs · Mathematics 2014-10-20 Xiao Yu , Xiao-Qiang Zhao

This paper is concerned with the spreading speeds of nonlocal dispersal predator-prey systems in shifting habitats under general initial conditions. By employing geometric optics techniques and theory of viscosity solutions, we reformulate…

Analysis of PDEs · Mathematics 2026-04-17 Wen Tao , Wan-Tong Li , Shigui Ruan , Wen-Bing Xu

We study the persistence and propagation (or blocking) phenomena for a species in periodically hostile environments. The problem is described by a reaction-diffusion equation with zero Dirichlet boundary condition. We first derive the…

Analysis of PDEs · Mathematics 2015-05-28 Jong-Shenq Guo , Francois Hamel

We take interest in a reaction-diffusion system which has been recently proposed [11] as a model for the effect of a road on propagation phenomena arising in epidemiology and ecology. This system consists in coupling a classical Fisher-KPP…

Analysis of PDEs · Mathematics 2015-09-08 Thomas Giletti , Léonard Monsaingeon , Maolin Zhou

Reaction-advection-diffusion equations, in periodic settings and with general type nonlinearities, admit a threshold known as the minimal speed of propagation. The minimal speed does not have an accessible formula when the nonlinearity is…

Analysis of PDEs · Mathematics 2020-01-17 Mohammad El Smaily , Chunhua Ou

We consider a reaction-diffusion model for a population structured in phenotype. We assume that the population lives in a heterogeneous periodic environment, so that a given phenotypic trait may be more or less fit according to the spatial…

Analysis of PDEs · Mathematics 2025-03-07 Nathanaël Boutillon , Luca Rossi

This paper is concerned with some nonlinear propagation phenomena for reaction-advection-diffusion equations with Kolmogrov-Petrovsky-Piskunov (KPP) type nonlinearities in general periodic domains or in infinite cylinders with oscillating…

Analysis of PDEs · Mathematics 2010-11-23 Mohammad El Smaily

The paper is concerned with the effect of the spatio-temporal heterogeneity on the principal eigenvalue of some linear time-periodic parabolic system. Various asymptotic behaviors of the principal eigenvalue and its monotonicity, as a…

Analysis of PDEs · Mathematics 2025-01-16 Shuang Liu

We study existence and uniqueness of travelling fronts, and asymptotic speed of propagation for a non local reaction diffusion equation with spatial and genetic trait structure.

Analysis of PDEs · Mathematics 2014-12-23 Henri Berestycki , Tianling Jin , Luis Silvestre

We study the existence and stability of propagating fronts in Meinhardt's multivariable reaction-diffusion model of branching in one spatial dimension. We identify a saddle-node-infinite-period (SNIPER) bifurcation of fronts that leads to…

Pattern Formation and Solitons · Physics 2023-05-18 Edgar Knobloch , Arik Yochelis

In this paper we study the invasion fronts of spatially periodic monotone reaction-diffusion systems in a multi-dimensional setting. We study the pulsating traveling waves that connect the trivial equilibrium, for which all components of…

Analysis of PDEs · Mathematics 2025-11-14 Liangliang Deng , Arnaud Ducrot , Quentin Griette

In this paper, we first focus on the speed selection problem for the reaction-diffusion equation of the monostable type. By investigating the decay rates of the minimal traveling wave front, we propose a sufficient and necessary condition…

Analysis of PDEs · Mathematics 2024-08-21 Chang-Hong Wu , Dongyuan Xiao , Maolin Zhou
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