Math @ Duke
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Publications [#316662] of James H. Nolen
Papers Published
- 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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