Comptes Rendus
no. 4
Mathematical analysis/Partial differential equations
An Ikehara-type theorem for functions convergent to zero
[Un théorème de type Ikehara pour les fonctions convergeant vers zéro]

Présenté par : Jean-Michel Coron

Dmitri Finkelshtein1 ; Pasha Tkachov2
1 Department of Mathematics, Swansea University, Bay Campus, Fabian Way, Swansea SA2 8EN, UK
2 Gran Sasso Science Institute, Viale Francesco Crispi, 7, 67100 L'Aquila AQ, Italy
Comptes Rendus. Mathématique, Volume 357 (2019) no. 4, pp. 333-338.

Nous établissons un analogue du théorème de Ikehara pour les fonctions positives non croissantes qui tendent vers zéro. En particulier, cela fournit une démonstration complète des énoncés formulés par Diekmann et Kaper (1978) [5] et par Carr et Chmaj (2004) [1], qui sont maintenant largement utilisés pour démontrer l'unicité des ondes progressives dans diverses équations de réaction–diffusion.

We establish an analogue of the Ikehara theorem for positive non-increasing functions convergent to zero. In particular, this provides a complete proof of the results formulated in Diekmann & Kaper (1978) [5] and Carr & Chmaj (2004) [1], which are widely used nowadays to prove the uniqueness of traveling waves for various reaction–diffusion equations.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2019.04.007
Dmitri Finkelshtein 1 ; Pasha Tkachov 2

1 Department of Mathematics, Swansea University, Bay Campus, Fabian Way, Swansea SA2 8EN, UK
2 Gran Sasso Science Institute, Viale Francesco Crispi, 7, 67100 L'Aquila AQ, Italy 
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Dmitri Finkelshtein; Pasha Tkachov. An Ikehara-type theorem for functions convergent to zero. Comptes Rendus. Mathématique, Volume 357 (2019) no. 4, pp. 333-338. doi : 10.1016/j.crma.2019.04.007. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2019.04.007/

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