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The FKPP equation with a variable growth rate and advection by an incompressible velocity field is considered as a model for plankton dispersed by ocean currents. If the average growth rate is negative then the model has a…

Populations and Evolution · Quantitative Biology 2007-09-04 Daniel A. Birch , Yue-Kin Tsang , William R. Young

We consider a nonlocal Fisher-KPP equation that models a population structured in space and in phenotype. The population lives in a heterogeneous periodic environment: the diffusion coefficient, the mutation coefficient and the fitness of…

Analysis of PDEs · Mathematics 2024-10-28 Nathanaël Boutillon

The propagation of a beneficial mutation in a spatially extended population is usually studied using the phenomenological stochastic Fisher-Kolmogorov (SFKPP) equation. We derive here an individual based, stochastic model founded on the…

Biological Physics · Physics 2017-08-02 Bahram Houchmandzadeh , Marcel Vallade

We study the Cauchy problem in the hyperbolic space for the heat equation with a Fisher-KPP type forcing term. Depending on the relative strength of diffusion, measured by the infimum of the spectrum of the Laplace-Beltrami operator, as…

Analysis of PDEs · Mathematics 2026-05-07 María del Mar González , Irene Gonzálvez , Fernando Quirós

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

The Fisher-KPP equation is a model for population dynamics that has generated a huge amount of interest since its introduction in 1937. The speed with which a population spreads has been computed quite precisely when the initial data decays…

Analysis of PDEs · Mathematics 2016-09-21 Christopher Henderson

We consider the traveling wave speed for Fisher-KPP (FKPP) fronts under the influence of repulsive chemotaxis and provide an almost complete picture of its asymptotic dependence on parameters representing the strength and length-scale of…

Analysis of PDEs · Mathematics 2023-08-07 Quentin Griette , Christopher Henderson , Olga Turanova

We consider the spreading dynamics of the Fisher-KPP equation in a shifting environment, by analyzing the limit of the rate function of the solutions. For environments with a weak monotone condition, it was demonstrated in a previous paper…

Analysis of PDEs · Mathematics 2024-10-21 King-Yeung Lam , Gregoire Nadin , Xiao Yu

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

In the work of Colliander et al. (2010), a minimal lattice model was constructed describing the transfer of energy to high frequencies in the defocusing nonlinear Schr\"odinger equation. In the present work, we present a systematic study of…

Pattern Formation and Solitons · Physics 2024-07-25 Ross Parker , Pierre Germain , Jesús Cuevas-Maraver , Alejandro Aceves , P. G. Kevrekidis

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

Analysis of the speed of propagation in parabolic operators is frequently carried out considering the minimal speed at which its traveling waves move. This value depends on the solution concept being considered. We analyze an extensive…

Analysis of PDEs · Mathematics 2022-07-14 Margarita Arias , Juan Campos

We study traveling waves of the KPP equation in the half-space with Dirichlet boundary conditions. We show that minimal-speed waves are unique up to translation and rotation but faster waves are not. We represent our waves as Laplace…

Analysis of PDEs · Mathematics 2023-08-15 Julien Berestycki , Cole Graham , Yujin H. Kim , Bastien Mallein

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 Fisher-KPP model, and generalisations thereof, is a simple reaction-diffusion models of biological invasion that assumes individuals in the population undergo linear diffusion with diffusivity $D$, and logistic proliferation with rate…

Pattern Formation and Solitons · Physics 2022-01-25 Maud El-Hachem , Scott W McCue , Matthew J Simpson

We construct the traveling wave solutions of an FKPP growth process of two densities of particles, and prove that the critical traveling waves are locally stable in a space where the perturbations can grow exponentially at the back of the…

Analysis of PDEs · Mathematics 2023-08-16 Florian Kreten

In this paper, we study the existence and stability of random transition waves for time heterogeneous Fisher-KPP Equations with nonlocal diffusion. More specifically, we consider general time heterogeneities both for the nonlocal diffusion…

Analysis of PDEs · Mathematics 2023-06-01 Min Zhao , Rong Yuan

In this paper, we investigate the stability and uniqueness of generalized traveling wave solutions of lattice Fisher-KPP equations with general time and space dependence. We first show the existence, uniqueness, and stability of strictly…

Dynamical Systems · Mathematics 2019-01-11 Feng Cao , Wenxian Shen

Incorporating free boundary into time-delayed reaction-diffusion equations yields a compatible condition that guarantees the well-posedness of the initial value problem. With the KPP type nonlinearity we then establish a vanishing-spreading…

Analysis of PDEs · Mathematics 2021-08-03 Ningkui Sun , Jian Fang

In this work we revisit the existence, stability and dynamics of unstable traveling solitary waves in the context of lattice dynamical systems. We consider a nonlinear lattice of an $\alpha$-Fermi-Pasta-Ulam type with the additional feature…

Pattern Formation and Solitons · Physics 2021-03-16 H. Duran , H. Xu , P. G. Kevrekidis , A. Vainchtein