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arXiv · 1302.1132

An extension of the Wright's 3/2-theorem for the KPP-Fisher delayed equation

Karel Hasik·Sergei Trofimchuk
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Abstract

We present a short proof of the following natural extension of the famous Wright's 3/2-stability theorem: the conditions $\tau \leq 3/2, \ c \geq 2$ imply the presence of the positive traveling fronts (not necessarily monotone) $u = \phi(x\cdot \nu+ct), \ |\nu| =1,$ in the delayed KPP-Fisher equation $u_t(t,x) = \Delta u(t,x) + u(t,x)(1-u(t-\tau,x))$, $u\geq 0,$ $x \in \R^m.$

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Karel Hasik, Sergei Trofimchuk. 2013-02-05. An extension of the Wright's 3/2-theorem for the KPP-Fisher delayed equation. https://doi.org/10.1090/s0002-9939-2015-12496-3

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