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arXiv · 1903.11274

Sharp large time behaviour in N -dimensional Fisher-KPP equations

Jean-Michel Roquejoffre·Luca Rossi·Violaine Roussier-Michon
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Abstract

We study the large time behaviour of the Fisher-KPP equation $\partial$ t u = $\Delta$u + u -- u 2 in spatial dimension N , when the initial datum is compactly supported. We prove the existence of a Lipschitz function s of the unit sphere, such that u(t, x) converges, as t goes to infinity, to U c * |x| -- c * t + N + 2 c * lnt + s $\infty$ x |x| , where U c * is the 1D travelling front with minimal speed c * = 2. This extends an earlier result of G{\"a}rtner.

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Jean-Michel Roquejoffre, Luca Rossi, Violaine Roussier-Michon. 2019-03-27. Sharp large time behaviour in N -dimensional Fisher-KPP equations. https://arxiv.org/abs/1903.11274

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