一类广义Camassa-Holm方程的无限传播速度与渐近行为（英文）  

Infinite propagation speed and asymptotic behavior for a generalized Camassa-Holm equation

作　　者：崔文军 韩励佳 王端 Cui Wenjun;Han Lijia;Wang Duan(Department of Mathematics and Physics,North China Electric Power University,Beijing 102206,China;Graduate School,China National Nuclear Corporation,Beijing 102413,China)

机构地区：[1]华北电力大学数理学院,北京102206 [2]中国核工业集团研究生部,北京102413

出　　处：《上海师范大学学报（自然科学版）》2018年第3期290-304,共15页Journal of Shanghai Normal University(Natural Sciences)

基　　金：Fundamental Research Funds for the Central Universities(2015MS53)

摘　　要：研究了一类广义的Camassa-Holm方程的Cauchy问题.首先,证明当初始值u_0(x)具有紧支集的情况下,方程的解u(x,t)不再具有紧支集.因此,由u_0(x)表示的具有紧支集的初始扰动的传播速度是无限的.其次,当x趋于无穷时,证明了方程的解u(x,t)具有指数衰减.最后,研究了当初始值为指数或代数衰减时,方程的解在无穷远处的渐近行为.This paper is devoted to the Cauchy problem for a generalized Camassa-Holm equation. First, we prove that the solution u（x t） to the generalized Camassa-Holm equation with compactly supported initial data uo（x） instantly loses compact support. In this sense, the localized disturbance represented by u0 propagates with an infinite speed. We further prove that the solution u（xt） to the generalized Camassa-Holm equation has an exponential decay as Ixl goes to infinity. Moreover, the asymptotic behaviors of the solution at infinity axe investigated as the initial data decays exponentially or algebraically.

关 键 词：广义的Camassa—Holm方程 无限速度传播 渐近行为 

分 类 号：O175.29[理学—数学]