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


Authors: Rafael D. Benguria and Abraham Solar
Journal: Proc. Amer. Math. Soc. 147 (2019), 2495-2501
MSC (2010): Primary 34K12; Secondary 35K57, 92D25
DOI: https://doi.org/10.1090/proc/14381
Published electronically: March 5, 2019
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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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Additional Information

Rafael D. Benguria
Affiliation: Instituto de Física, Pontificia Universidad Católica de Chile, Casilla 306, Santiago, Chile
Email: rbenguri@fis.uc.cl

Abraham Solar
Affiliation: Instituto de Física, Pontificia Universidad Católica de Chile, Casilla 306, Santiago, Chile
Email: asolar@fis.uc.cl

DOI: https://doi.org/10.1090/proc/14381
Keywords: Semi-wavefront stability, semi-wavefront uniqueness, delay, reaction-diffusion equations
Received by editor(s): June 7, 2018
Received by editor(s) in revised form: July 16, 2018
Published electronically: March 5, 2019
Additional Notes: This work was supported by FONDECYT (Chile) through the Postdoctoral Fondecyt 2016 program with project number 3160473, and FONDECYT project 116–0856.
Communicated by: Catherine Sulem
Article copyright: © Copyright 2019 American Mathematical Society