摘要
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.
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.
基金
supported by NSF grant DMS-1351653,NSF grant DMS-1311903
the European Union’s Seventh Framework Programme(FP/2007-2013)/ERC Grant Agreement n.321186-Rea Di-“Reaction-Diffusion Equations,Propagation and Modelling”
ANR project NONLOCAL ANR-14-CE25-0013
