[Sur la stabilité de l'état 1 dans l'équation de Fisher–KPP non locale en domaine borné]
Nous considérons l'équation de Fisher–KPP non locale en domaine borné, avec conditions de Neumann au bord. À l'aide d'une fonction de Lyapunov, nous montrons que, sous une hypothèse générale sur le noyau présent dans le terme non local, l'état stationnaire 1 est globalement asymptotiquement stable. Cette hypothèse se trouve être reliée à certaines conditions données dans la littérature, qui assurent que les fronts de propagation relient 0 et 1.
We consider the non-local Fisher–KPP equation on a bounded domain with Neumann boundary conditions. Thanks to a Lyapunov function, we prove that, under a general hypothesis on the kernel involved in the non-local term, the homogenous steady state 1 is globally asymptotically stable. This assumption happens to be linked to some conditions given in the literature, which ensure that travelling waves link 0 to 1.
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@article{CRMATH_2018__356_6_644_0,
author = {Pouchol, Camille},
title = {On the stability of the state 1 in the non-local {Fisher{\textendash}KPP} equation in bounded domains},
journal = {Comptes Rendus. Math\'ematique},
pages = {644--647},
publisher = {Elsevier},
volume = {356},
number = {6},
year = {2018},
doi = {10.1016/j.crma.2018.04.016},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2018.04.016/}
}
TY - JOUR AU - Pouchol, Camille TI - On the stability of the state 1 in the non-local Fisher–KPP equation in bounded domains JO - Comptes Rendus. Mathématique PY - 2018 SP - 644 EP - 647 VL - 356 IS - 6 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2018.04.016/ DO - 10.1016/j.crma.2018.04.016 LA - en ID - CRMATH_2018__356_6_644_0 ER -
%0 Journal Article %A Pouchol, Camille %T On the stability of the state 1 in the non-local Fisher–KPP equation in bounded domains %J Comptes Rendus. Mathématique %D 2018 %P 644-647 %V 356 %N 6 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2018.04.016/ %R 10.1016/j.crma.2018.04.016 %G en %F CRMATH_2018__356_6_644_0
Pouchol, Camille. On the stability of the state 1 in the non-local Fisher–KPP equation in bounded domains. Comptes Rendus. Mathématique, Tome 356 (2018) no. 6, pp. 644-647. doi : 10.1016/j.crma.2018.04.016. http://www.numdam.org/articles/10.1016/j.crma.2018.04.016/
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