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| Convergence to a Single Wave in the Fisher-KPP Equation |
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Citation： |
James NOLEN,Jean-Michel ROQUEJOFFRE,Lenya RYZHIK.Convergence to a Single Wave in the Fisher-KPP Equation[J].Chinese Annals of Mathematics B,2017,38(2):629~646 |
| Page view： 992
Net amount： 670 |
Authors： |
James NOLEN; Jean-Michel ROQUEJOFFRE;Lenya RYZHIK |
Foundation： |
This work was supported by NSF grant DMS-1351653, NSF grant
DMS-1311903 and the European Union's Seventh Framework Programme
(FP/2007-2013) / ERC Grant Agreement n. 321186 - ReaDi -
``Reaction-Diffusion Equations, Propagation and Modelling'', as well
as the ANR project NONLOCAL ANR-14-CE25-0013. |
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| 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 $2t
- \big(\frac32\big) \log t +x_\infty$, the solution of the equation
converges as $t\to+\infty$ to a translate of the traveling wave
corresponding to the minimal speed~$c_*=2$. The constant $x_\infty$
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. |
Keywords： |
Traveling waves, KPP, Front propagation, Asymptotic analysis,Reaction-diffusion |
Classification： |
35K57, 35C07, 35B40 |
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