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Article Dans Une Revue Networks and Heterogeneous Media Année : 2013

A short proof of the logarithmic Bramson correction in Fisher-KPP equations

Résumé

In this paper, we explain in simple PDE terms a famous result of Bramson about the loga- rithmic 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 of the minimal front, with and without the logarithmic delay. Our analysis also yields the large-time convergence of the solutions u along their level sets to the profile of the minimal travelling front.
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Dates et versions

hal-00815553 , version 1 (19-04-2013)

Identifiants

Citer

Francois Hamel, James Nolen, Jean-Michel Roquejoffre, Lenya Ryzhik. A short proof of the logarithmic Bramson correction in Fisher-KPP equations. Networks and Heterogeneous Media, 2013, 8 (1), pp.275-279. ⟨10.3934/nhm.2013.8.275⟩. ⟨hal-00815553⟩
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