Dans cet article, nous considérons l'équation de Fisher-KPP non locale, qui modélise la dynamique d'une population ou la force de compétition pour les ressources dépend de la distance entre les individus. Nous obtenons une asymptotique précise en temps long de la position d'une population qui est initialement localisée en espace. Selon la décroissance à l'infini du noyau de compétition, la position du front est soit
We consider the non-local Fisher-KPP equation modeling a population with individuals competing with each other for resources with a strength related to their distance, and obtain the asymptotics for the position of the invasion front starting from a localized population. Depending on the behavior of the competition kernel at infinity, the location of the front is either
Mots-clés : Reaction-diffusion equations, Logarithmic delay, Parabolic Harnack inequality
@article{AIHPC_2020__37_1_51_0, author = {Bouin, Emeric and Henderson, Christopher and Ryzhik, Lenya}, title = {The {Bramson} delay in the non-local {Fisher-KPP} equation}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {51--77}, publisher = {Elsevier}, volume = {37}, number = {1}, year = {2020}, doi = {10.1016/j.anihpc.2019.07.001}, mrnumber = {4049916}, zbl = {1436.35239}, language = {en}, url = {https://www.numdam.org/articles/10.1016/j.anihpc.2019.07.001/} }
TY - JOUR AU - Bouin, Emeric AU - Henderson, Christopher AU - Ryzhik, Lenya TI - The Bramson delay in the non-local Fisher-KPP equation JO - Annales de l'I.H.P. Analyse non linéaire PY - 2020 SP - 51 EP - 77 VL - 37 IS - 1 PB - Elsevier UR - https://www.numdam.org/articles/10.1016/j.anihpc.2019.07.001/ DO - 10.1016/j.anihpc.2019.07.001 LA - en ID - AIHPC_2020__37_1_51_0 ER -
%0 Journal Article %A Bouin, Emeric %A Henderson, Christopher %A Ryzhik, Lenya %T The Bramson delay in the non-local Fisher-KPP equation %J Annales de l'I.H.P. Analyse non linéaire %D 2020 %P 51-77 %V 37 %N 1 %I Elsevier %U https://www.numdam.org/articles/10.1016/j.anihpc.2019.07.001/ %R 10.1016/j.anihpc.2019.07.001 %G en %F AIHPC_2020__37_1_51_0
Bouin, Emeric; Henderson, Christopher; Ryzhik, Lenya. The Bramson delay in the non-local Fisher-KPP equation. Annales de l'I.H.P. Analyse non linéaire, Tome 37 (2020) no. 1, pp. 51-77. doi : 10.1016/j.anihpc.2019.07.001. https://www.numdam.org/articles/10.1016/j.anihpc.2019.07.001/
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