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- W4300521054 abstract "We consider the one-dimensional Fisher-KPP equation with step-like initial data. Nolen, Roquejoffre, and Ryzhik showed that the solution $u$ converges at long time to a traveling wave $phi$ at a position $tilde sigma(t) = 2t - (3/2)log t + alpha_0- 3sqrt{pi}/sqrt{t}$, with error $O(t^{gamma-1})$ for any $gamma>0$. With their methods, we find a refined shift $sigma(t) = tilde sigma(t) + mu_* (log t)/t + alpha_1/t$ such that in the frame moving with $sigma$, the solution $u$ satisfies $u(t,x) = phi (x) + psi(x)/t + O(t^{gamma-3/2})$ for a certain profile $psi$ independent of initial data. The coefficient $alpha_1$ depends on initial data, but $mu_* = 9(5-6log 2)/8$ is universal, and agrees with a finding of Berestycki, Brunet, and Derrida in a closely-related problem. Furthermore, we predict the asymptotic forms of $sigma$ and $u$ to arbitrarily high order." @default.
- W4300521054 created "2022-10-03" @default.
- W4300521054 creator A5088824905 @default.
- W4300521054 date "2017-12-06" @default.
- W4300521054 modified "2023-09-25" @default.
- W4300521054 title "Precise asymptotics for Fisher-KPP fronts" @default.
- W4300521054 doi "https://doi.org/10.48550/arxiv.1712.02472" @default.
- W4300521054 hasPublicationYear "2017" @default.
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