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

Abstract

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

8 pages, submitted

References in corpus (1)

• Slowly oscillating wavefronts of the KPP-Fisher delayed equation

Cited by in corpus (5)

• Slowly oscillating wavefronts of the KPP-Fisher delayed equation
• Traveling waves in the nonlocal KPP-Fisher equation: different roles of the right and the left interactions
• A simple approach to the wave uniqueness problem
• A note on the existence of non-monotone non-oscillating wavefronts
• On the geometric diversity of wavefronts for the scalar Kolmogorov ecological equation