Remark on the well-posedness of weakly dispersive equations

Jiao He; Youcef Mammeri

doi:10.1051/proc/201864111

All issues

Volume 64 (2018)

ESAIM: ProcS, 64 (2018) 111-120

Abstract

Open Access

Issue		ESAIM: ProcS Volume 64, 2018 SMAI 2017 - 8^e Biennale Française des Mathématiques Appliquées et Industrielles


Page(s)		111 - 120
DOI		https://doi.org/10.1051/proc/201864111
Published online		20 November 2018

ESAIM: PROCEEDINGS AND SURVEYS, October 2018, Vol. 64, p. 111-120

Remark on the well-posedness of weakly dispersive equations

Jiao He¹ and Youcef Mammeri²^,3

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

Abstract

We improve the results about the well-posedness of the regularized fractional dispersive equation (1 + D_x^α)u_t + u_x + uu_x = 0 when 0 < α ≤ 1. When #x03B1; < 1, the existence and uniqueness of vanishing viscosity solution is proved.

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