Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5772385 | Journal of Functional Analysis | 2017 | 29 Pages |
Abstract
We give descriptions of the family Ïs,sâ[0,s0] through the single pair of functions Ï0(x) and Ïs0(x), as extremal solutions of the Kolmogorov-Petrovskii-Piskunov (KPP) travelling wave equation on the half-line, through a martingale representation, and as a single explicit series expansion. We also obtain a precise result concerning the tail behaviour of K(â). In addition, in the regime where K(â)>0 almost surely, we show that u(x,t):=Px(K(t)=0) suitably centred converges to the KPP critical travelling wave on the whole real line.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Julien Berestycki, Ãric Brunet, Simon C. Harris, Piotr MiÅoÅ,