Nous étudions le problème de Cauchy associé à lʼéquation de Benjamin–Ono avec dispersion généralisée. Notre objectif est dʼétablir les propriétés de persistance de la solution dans des espaces de Sobolev avec poids et dʼen déduire quelques propriétés de prolongement unique pour ses solutions. En particulier, nous établirons un taux de décroissance optimal pour les solutions de ce modèle.
We study the initial value problem associated to the dispersion generalized Benjamin–Ono equation. Our aim is to establish persistence properties of the solution flow in weighted Sobolev spaces and to deduce from them some sharp unique continuation properties of solutions to this equation. In particular, we shall establish optimal decay rate for the solutions of this model.
Mots-clés : Benjamin–Ono equation, Weighted Sobolev spaces
@article{AIHPC_2013__30_5_763_0, author = {Fonseca, Germ\'an and Linares, Felipe and Ponce, Gustavo}, title = {The {IVP} for the dispersion generalized {Benjamin{\textendash}Ono} equation in weighted {Sobolev} spaces}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {763--790}, publisher = {Elsevier}, volume = {30}, number = {5}, year = {2013}, doi = {10.1016/j.anihpc.2012.06.006}, mrnumber = {3103170}, zbl = {06295441}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.anihpc.2012.06.006/} }
TY - JOUR AU - Fonseca, Germán AU - Linares, Felipe AU - Ponce, Gustavo TI - The IVP for the dispersion generalized Benjamin–Ono equation in weighted Sobolev spaces JO - Annales de l'I.H.P. Analyse non linéaire PY - 2013 SP - 763 EP - 790 VL - 30 IS - 5 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpc.2012.06.006/ DO - 10.1016/j.anihpc.2012.06.006 LA - en ID - AIHPC_2013__30_5_763_0 ER -
%0 Journal Article %A Fonseca, Germán %A Linares, Felipe %A Ponce, Gustavo %T The IVP for the dispersion generalized Benjamin–Ono equation in weighted Sobolev spaces %J Annales de l'I.H.P. Analyse non linéaire %D 2013 %P 763-790 %V 30 %N 5 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpc.2012.06.006/ %R 10.1016/j.anihpc.2012.06.006 %G en %F AIHPC_2013__30_5_763_0
Fonseca, Germán; Linares, Felipe; Ponce, Gustavo. The IVP for the dispersion generalized Benjamin–Ono equation in weighted Sobolev spaces. Annales de l'I.H.P. Analyse non linéaire, Tome 30 (2013) no. 5, pp. 763-790. doi : 10.1016/j.anihpc.2012.06.006. http://www.numdam.org/articles/10.1016/j.anihpc.2012.06.006/
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