[Unicité des solutions de l’équation de Camassa–Holm dans un domaine ouvert]
Nous montrons l’unicité des solutions de l’équation de Camassa–Holm sur un intervalle fini avec des conditions non-homogènes pour des solutions de moment d’inertie borné. Nous établissons aussi un résultat similaire pour les équations de Camassa–Holm d’ordre supérieur. Nos preuves s’appuient sur des méthodes d’énergies, avec des symétriseurs qui sont donnés comme solutions d’équations elliptiques auxiliaires bien choisies.
We establish the uniqueness of solutions of the Camassa–Holm equation on a finite interval with non-homogeneous boundary conditions in the case of bounded momentum. A similar result for the higher-order Camassa–Holm system is also given. Our proofs rely on energy-type methods, with some multipliers given as solutions of some auxiliary elliptic systems.
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Mots-clés : Camassa–Holm, condition au bord non-homogène, couplage elliptique-hyperbolique
Florent Noisette 1
CC-BY 4.0
@article{CRMATH_2025__363_G2_139_0,
author = {Florent Noisette},
title = {Uniqueness for the {Camassa{\textendash}Holm} equation with non-homogeneous boundary conditions},
journal = {Comptes Rendus. Math\'ematique},
pages = {139--168},
publisher = {Acad\'emie des sciences, Paris},
volume = {363},
year = {2025},
doi = {10.5802/crmath.664},
language = {en},
}
Florent Noisette. Uniqueness for the Camassa–Holm equation with non-homogeneous boundary conditions. Comptes Rendus. Mathématique, Volume 363 (2025), pp. 139-168. doi : 10.5802/crmath.664. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.664/
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