An iterative estimation for disturbances of semi-wavefronts to the delayed Fisher-KPP equation

Benguria, Rafael; Solar, Abraham

doi:10.1090/proc/14381

An iterative estimation for disturbances of semi-wavefronts to the delayed Fisher-KPP equation
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by Rafael D. Benguria and Abraham Solar PDF

Proc. Amer. Math. Soc. 147 (2019), 2495-2501 Request permission

Abstract:

We give an iterative method to estimate the disturbance of semi-wavefronts of the equation $\dot {u}(t,x) = u''(t,x) +u(t,x)(1-u(t-h,x)),$ $x \in \mathbb {R},\ t >0$, where $h>0.$ As a consequence, we show the exponential stability, with an unbounded weight, of semi-wavefronts with speed $c\geq 2\sqrt {2}$ and $h>0$. Under the same restriction of $c$ and $h$, the uniqueness of semi-wavefronts is obtained.

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