Abstract
We study the stability properties of semi-wavefronts of the KPP-Fisher equation with infinite delay \(\frac{\partial }{\partial t}u(t, x)=\frac{\partial ^2 }{\partial x^2}u(t, x)+\int _{0}^{+\infty }u(t-s, x)d\mu _1(s)\Big (1-\int _0^{+\infty }u(t-s, x)d\mu _2(s)\Big ), \, t>0, \, x\in {\mathbb R},\) where \(\mu _1\) and \(\mu _2\) are Borel measures. We show an interesting property about the non convergence in form when the delay is finite, unlike the classic convergence result to KPP-Fisher equation without delay. We also present a result about the stability of semi-wavefronts to the Neutral KPP-Fisher equation.
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Acknowledgements
It is a pleasure to thank Sergei Trofimchuk for many valuable discussions. This research was supported by Fondecyt (Chile) #11190350.
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Solar, A. Stability of Solutions to Functional KPP-Fisher Equations. J Dyn Diff Equat (2023). https://doi.org/10.1007/s10884-023-10297-9
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DOI: https://doi.org/10.1007/s10884-023-10297-9