【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.更多还原

【Abstract】 The limit behavior of the solution to a kind of new nonlinear dispersive shallow water wave(equation) with strong dispersive term is studied.It combines the linear dispersion of Korteweg-de Veris(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 |u_x|,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.更多还原