一类带强色散项DGH方程解的极限问题  

Limit behavior of solution to DGH equation with strong dispersive term

作　　者：方国昌[1] 田立新[1] 桂贵龙[1] 

机构地区：[1]江苏大学非线性科学研究中心,江苏镇江212013

出　　处：《江苏大学学报（自然科学版）》2006年第2期176-180,共5页Journal of Jiangsu University：Natural Science Edition

基　　金：国家自然科学基金资助项目(10071033);江苏省自然科学基金资助项目(BK2002003)

摘　　要：研究一类新的非线性色散浅水波DGH方程带强色散项的极限问题,方程结合KdV方程的线性色散项和C-H方程的非线性(非局部)色散项.研究了方程柯西问题的全局适定性.在初值问题的一个简单假设下,得到在索伯列夫空间(HS,s≥3)中方程解的的全局存在性,主要研究了当γ→0时的极限情况.运用先验估计,利用对|ux|一致有界的全局估计,得出在L2中方程的解u(与γ有关)是一柯西序列,因而收敛到HS(s≥3)中C-H方程的解.The limit behavior of the solution to equation with strong dispersive term is studied. a kind of new nonlinear dispersive shallow water wave It combines the linear dispersion of Korteweg-de Veils equation with the nonlinear（nonlocal） dispersion of the Camassa-Holm equation. Under the assumption of a simple condition on the initial data, the higher Sobolev space（H^s, s≥3） is required to obtain the global existence for the solution of the equation. The issue of the limit as γ tends to zero is investigated. By using the global estimate of the uniform bound for ｜us｜, it shows that the solution of the equation with respect to γ is a Cauchy sequence in L^2 and therefore is convergent to the solution of the C - H equation in H^s, for s≥3.

关 键 词：DGH方程 peakon解 哈密顿算子 先验估计 可积性 

分 类 号：O175[理学—数学]