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arXiv · 2609.32051

Large time behaviour in the multidimensional nonlocal Fisher-KPP equation

Jean-Michel Roquejoffre·Mingmin Zhang
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Abstract

This work studies the expansion of the level sets of the solutions of a Fisher-KPP type reaction- diffusion equation, the diffusion being given by a nonnegative, compactly supported, even kernel. Because the latter is not assumed to be spherically symmetric, the level sets advance at an asymptotic speed given by a Freidlin-Gärtner type formula. The main contribution of this paper is to push the expansion up to terms that vanish as time goes to infinity, consisting in an asymptotically logarithmic delay corrected by an function that is constant in time, but depends on the direction of propagation.

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Jean-Michel Roquejoffre, Mingmin Zhang. 2026-09-25. Large time behaviour in the multidimensional nonlocal Fisher-KPP equation. https://arxiv.org/abs/2609.32051

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