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Publications [#316662] of James H. Nolen

Papers Published

  1. Nolen, J; Roquejoffre, J-M; Ryzhik, L, Convergence to a single wave in the Fisher-KPP equation, Chinese Annals of Mathematics, Series B, vol. 38 no. 2 (2017), pp. 629-646, Springer Nature [1604.02994], [doi]
    (last updated on 2024/03/28)

    Abstract:
    The authors 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. The constant x∞ depends on the initial condition u(0, x). The proof is elaborate, and based on probabilistic arguments. The purpose of this paper is to provide a simple proof based on PDE arguments.

 

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