The Bramson delay in the non-local Fisher-KPP equation
نویسندگان
چکیده
منابع مشابه
The Bramson delay in the non-local Fisher-KPP equation
We consider the non-local Fisher-KPP equation modeling a population with individuals competing with each other for resources with a strength related to their distance, and obtain the asymptotics for the position of the invasion front starting from a localized population. Depending on the behavior of the competition kernel at infinity, the location of the front is either 2t− (3/2) log t+O(1), as...
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We consider the Fisher-KPP equation with a nonlocal saturation effect defined through an interaction kernel φ(x) and investigate the possible differences with the standard Fisher-KPP equation. Our first concern is the existence of steady states. We prove that if the Fourier transform φ̂(ξ) is positive or if the length σ of the nonlocal interaction is short enough, then the only steady states are...
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In this paper, we explain in simple PDE terms a famous result of Bramson about the logarithmic delay of the position of the solutions u(t, x) of Fisher-KPP reaction-diffusion equations in R, with respect to the position of the travelling front with minimal speed. Our proof is based on the comparison of u to the solutions of linearized equations with Dirichlet boundary conditions at the position...
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We study the large time asymptotics of a solution of the Fisher-KPP reaction-diffusion equation, with an initial condition that is a compact perturbation of a step function. A well-known result of Bramson states that, in the reference frame moving as 2t− (3/2) log t+x∞, the solution of the equation converges as t→ +∞ to a translate of the traveling wave corresponding to the minimal speed c∗ = 2...
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ژورنال
عنوان ژورنال: Annales de l'Institut Henri Poincaré C, Analyse non linéaire
سال: 2020
ISSN: 0294-1449
DOI: 10.1016/j.anihpc.2019.07.001