Issue |
ESAIM: ProcS
Volume 64, 2018
SMAI 2017 - 8e Biennale Française des Mathématiques Appliquées et Industrielles
|
|
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Page(s) | 111 - 120 | |
DOI | https://doi.org/10.1051/proc/201864111 | |
Published online | 20 November 2018 |
Remark on the well-posedness of weakly dispersive equations
1
Institut Camille Jordan, CNRS UMR 5208, Université Claude Bernard Lyon 1, 69622 Villeurbanne, France ; e-mail: jiao.he@math.univ-lyon1.fr
2
Laboratoire Amiénois de Mathématique Fondamentale et Appliquée, CNRS UMR 7352, Université de Picardie Jules Verne, 80069 Amiens, France
3
Institut de Génétique, Environnement et Protection des Plantes, INRA UMR 1349, 35650 Le Rheu, France ; e-mail: youcef.mammeri@u-picardie.fr
We improve the results about the well-posedness of the regularized fractional dispersive equation (1 + Dxα)ut + ux + uux = 0 when 0 < α ≤ 1. When #x03B1; < 1, the existence and uniqueness of vanishing viscosity solution is proved.
© EDP Sciences, SMAI 2018
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