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

We give an iterative method to estimate the disturbance of semi-wavefronts of the equation: $\dot{u}(t,x)=u^{\mathrm{\prime }\mathrm{\prime }}(t,x)+u(t,x)(1-u(t-h,x)),$ $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 $c>2\sqrt{2}$ and $h>0$. Under the same restriction of $c$ and $h$, the uniqueness of semi-wavefronts is obtained.