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Related papers: Asymptotic spreading for Fisher-KPP reaction-diffu…

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We consider reaction-diffusion equations $\partial_tu=\Delta u+f(u)$ in the whole space $\mathbb{R}^N$ and we are interested in the large-time dynamics of solutions ranging in the interval $[0,1]$, with general unbounded initial support.…

Analysis of PDEs · Mathematics 2022-07-14 François Hamel , Luca Rossi

The aim of this paper is to study the generalized Fisher-KPP equation with nonlocal diffusion. In specific we prove the existence of a critical speed so that traveling front type solutions exist up to this critical speed and non-existence…

Analysis of PDEs · Mathematics 2021-04-28 José Fuentealba , Alexander Quaas

In Cao, Du, Li and Li [8], a nonlocal diffusion model with free boundaries extending the local diffusion model of Du and Lin [12] was introduced and studied. For Fisher-KPP type nonlinearities, its long-time dynamical behaviour is shown to…

Analysis of PDEs · Mathematics 2020-01-28 Yihong Du , Fang Li , Maolin Zhou

The goal of this paper is to find the homogenized equation of a heterogenous Fisher-KPP model in a periodic medium. The solutions of this model are pulsating travelling fronts whose \emph{speeds} are superior to a parametric minimal speed…

Analysis of PDEs · Mathematics 2012-02-01 Mohammad El Smaily

This paper is concerned with transition fronts for reaction-diffusion equations of the Fisher-KPP type. Basic examples of transition fronts connecting the unstable steady state to the stable one are the standard traveling fronts, but the…

Analysis of PDEs · Mathematics 2014-04-11 Francois Hamel , 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 current paper is devoted to the study of spreading speeds and transition fronts of lattice KPP equations in time heterogeneous media. We first prove the existence, uniqueness, and stability of spatially homogeneous entire positive…

Dynamical Systems · Mathematics 2017-01-10 Feng Cao , Wenxian Shen

This paper establishes the spectral stability in exponentially weighted spaces of smooth traveling monotone fronts for reaction diffusion equations of Fisher-KPP type with nonlinear degenerate diffusion coefficient. It is assumed that the…

Analysis of PDEs · Mathematics 2017-06-02 J. Francisco Leyva , Ramon G. Plaza

In this paper, we investigate propagation phenomena for KPP bulk-surface systems in a cylindrical domain with general section and heterogeneous coefficients. As for the scalar KPP equation, we show that the asymptotic spreading speed of…

Analysis of PDEs · Mathematics 2022-09-01 Beniamin Bogosel , Thomas Giletti , Andrea Tellini

This article is concerned with the rigorous validation of anomalous spreading speeds in a system of coupled Fisher-KPP equations of cooperative type. Anomalous spreading refers to a scenario wherein the coupling of two equations leads to…

Analysis of PDEs · Mathematics 2015-07-22 Matt Holzer

Recently it has been shown that when an equation that allows so-called pulled fronts in the mean-field limit is modelled with a stochastic model with a finite number $N$ of particles per correlation volume, the convergence to the speed…

Statistical Mechanics · Physics 2009-11-07 Debabrata Panja

In this paper we consider a model for the diffusion of a population in a strip-shaped field, where the growth of the species is governed by a Fisher-KPP equation and which is bounded on one side by a road where the species can have a…

Analysis of PDEs · Mathematics 2015-06-30 Andrea Tellini

This paper is devoted to the analysis of the large-time behavior of solutions of one-dimensional Fisher-KPP reaction-diffusion equations. The initial conditions are assumed to be globally front-like and to decay at infinity towards the…

Analysis of PDEs · Mathematics 2009-06-18 Francois Hamel , Lionel Roques

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

We study numerically the evolution of one-dimensional FKPP fronts initiated from steep initial conditions in the presence of a quenched random growth rate. Compared to both the homogeneous case (with velocity $v_0$) and deterministic…

Disordered Systems and Neural Networks · Physics 2026-05-15 Ulysse Marquis , Henri Berestycki , Marc Barthelemy

We investigate the influence of fluid flows on the propagation of chemical fronts arising in FKPP type models. We develop an asymptotic theory for the front speed in a cellular flow in the limit of small molecular diffusivity and fast…

Fluid Dynamics · Physics 2014-07-16 Alexandra Tzella , Jacques Vanneste

Our investigation focuses on the asymptotic spreading behavior of the Fisher-KPP equation with a mixed local-nonlocal operator in the diffusion (see the work by X. Cabr\'e and J.-M. Roquejoffre, 2013, ref.[8]) to the setting of mixed…

Analysis of PDEs · Mathematics 2025-09-01 Begoña Barrios , Bryan Pichucho , Alexander Quaas

We study the asymptotic speed of traveling fronts of the scalar reaction diffusion for positive reaction terms and with a diffusion coefficient depending nonlinearly on the concentration and on its gradient. We restrict our study to…

Analysis of PDEs · Mathematics 2018-07-06 R. D. Benguria , M. C. Depassier

The famous Fisher-KPP reaction diffusion model combines linear diffusion with the typical Fisher-KPP reaction term, and appears in a number of relevant applications. It is remarkable as a mathematical model since, in the case of linear…

Analysis of PDEs · Mathematics 2016-07-06 Alessandro Audrito , Juan Luis Vazquez

We study the radially symmetric high dimensional Fisher-KPP nonlocal diffusion equation with free boundary, and reveal some fundamental differences from its one dimensional version considered in \cite{cdjfa} recently. Technically, this high…

Analysis of PDEs · Mathematics 2021-02-11 Yihong Du , Wenjie Ni