具有边界影响和非凸条件的广义BBM-Burgers方程的解的渐近性态  

Asymptotic behaviors of solutions for the generalized BBM-Burgers equation with boundary effect and Non-convexity

作　　者：叶芳慧[1] 

机构地区：[1]玉林师范学院数信学院,广西玉林537000

出　　处：《暨南大学学报（自然科学与医学版）》2012年第1期23-28,共6页Journal of Jinan University(Natural Science & Medicine Edition)

基　　金：国家自然科学基金项目(11161051);玉林师范学院青年基金项目(2009YJQN15)

摘　　要：研究具有边界影响且流函数为非凸条件下广义BBM-Burgers方程ut+f(u)x=uxx+uxxt的解的渐近性态.用L2-加权能量法证明了在初始值为小扰动的条件下,相应的初边值问题解的整体存在性及其解渐近收敛到一个驻波或一个稀疏波或这两种非线性波的叠加.The asymptotic behaviors of solutions are studied for the generalized BBM-Burgers equation u1 ＋f（u）x = uxx ＋ uxxx with boundary effect and Non-convexity in this paper. Under the condition that the initial and boundary data have small perturbation, using an L^2-energy method proves that the global solu- tion of corresponding general initial-boundary value problem exists and converges time-asymptotically to a stationary wave or a rarefaction wave or the superposition of these two kinds of wave for the generalized BBM-Burgers equation with one-side boundary effect.

关 键 词：广义BBM-BURGERS方程 初边值问题 解的渐近性态 先验估计 驻波 稀疏波 

分 类 号：O175.27[理学—数学]