Logarithmic Bramson correction for multi-dimensional periodic Fisher-KPP equations

2019/10/17 by Beniada Shabani, Shabani, Beniada · 1 citation
Medicine · Mathematics · #Mathematical and Theoretical Epidemiology and Ecology Models #Differential Equations and Numerical Methods #Fractional Differential Equations Solutions

paper · pdf · doi:10.48550/arxiv.1910.08178

Abstract

We study the long time behavior of solutions of periodic Fisher-KPP type equations in ℝⁿ that arise from compactly supported initial data. We prove that propagation along a fixed direction e∈\mathbbS^n-1 is completely determined by an associated minimizing direction e' which is unique and in a bijective correspondence with e. This correspondence allows us to determine the correct Bramson shift in higher dimensions and show that that the propagation along each e occurs asymptotically at the speed w_*(e)t-(n/2+1)/(λ_*(e') e⋅ e')log t+O(1).

Citations

• Multidimensional nonlinear diffusion arising in population genetics
• A new proof of Moser's parabolic harnack inequality using the old ideas of Nash

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• A shape theorem for BBM in a periodic environment

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