An initial-boundary-value problem that approximate the quarter-plane problem for the Korteweg-de Vries equation
نویسندگان
چکیده
Résumé Nous continuons l’étude du problème de Cauchy et aux limites pour l’équation de Korteweg-de Vries initiée dans [9]. On obtient des effets régularisants globaux uniformes par rapport à la longueur de l’intervalle et nous montrons que la solution du problème aux limites converge, lorsque la longueur de l’intervalle tend vers l’infini, vers la solution du problème posé sur le quart de plan t > 0, x > 0. Nous proposons un schéma aux différences finies très simple pour le problème sur [0, 1] et montrons sa stabilité.
منابع مشابه
The initial boundary problem for the Korteweg – de Vries equation on the negative quarter - plane
The initial boundary-value problem for the Korteweg–de Vries (KdV) equation on the negative quarter-plane, x < 0 and t > 0, is considered. The formulation of this problem is different to the usual initial boundary-value problem on the positive quarter-plane, for which x > 0 and t > 0. Two boundary conditions are required at x = 0 for the negative quarter-plane problem, in contrast to the one bo...
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