中文摘要：

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（H^s,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｜us｜一致有界的全局估计，得出在L^2中方程的解u（与γ有关）是一柯西序列，因而收敛到H^s（s≥3）中C—H方程的解．

英文摘要：

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.