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

Hasik, Karel; Trofimchuk, Sergei

doi:10.1090/S0002-9939-2015-12496-3

An extension of Wright’s 3/2-theorem for the KPP-Fisher delayed equation
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by Karel Hasik and Sergei Trofimchuk

Proc. Amer. Math. Soc. 143 (2015), 3019-3027

DOI: https://doi.org/10.1090/S0002-9939-2015-12496-3

Published electronically: February 13, 2015

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Abstract:

We present a short proof of the following natural extension of Wright’s famous $3/2$-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 $u_t(t,x) = \Delta u(t,x) + u(t,x)(1-u(t-\tau ,x)),$ $u \geq 0,$ $x \in \mathbb {R}^m.$

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