带一般边界和大初始扰动条件的广义BBM-Burgers方程解的渐近性态  

Asymptotic behaviors of solutions for generalized BBM-Burgers equation with a general boundary and large initial disturbance

作　　者：陈诚[1] 

机构地区：[1]暨南大学信息科学技术学院数学系,广东广州510632

出　　处：《暨南大学学报（自然科学与医学版）》2012年第5期455-460,共6页Journal of Jinan University(Natural Science & Medicine Edition)

基　　金：国家自然科学基金资助项目(10871082)

摘　　要：研究广义BBM-Burgers方程ut+f(u)x=uxx+uxxt的一般初边值问题,其边界满足u(0,t)=u-(t)→u-(t→∞),u-(t)-u-≤0;初始值满足u(x,0)=u0(x)→u+(x→∞),u-(0)=u0(0)且u-<0<u+.在流函数f满足f″(u)>0,f'(0)=f(0)=0以及初边值为大扰动的条件下,用L2-能量方法证明其解的整体存在性及渐近收敛于强稳定波和强稀疏波的叠加.This paper is concerned with the initial-boundary value problem for the generalized BBM- Burgers equation ut＋f（u）x=uxx＋uxxt, with the general boundary condition u（0,t）=u_（t）→u_（t→∞）,u_（t）-u_≤0 and the initial date satisfingu（x,0）=u0（x）→u＋（x→∞）,u_（0）=u0（0）且u_〈0〈u＋. Under the condition that the flux functionfsatisfies f″（u）〉0,f′（0）=f（0）=0. we prove that the global solution exists and converges time-asymptotically to the superposition of a strong stationary wave and a strong rarefaction wave for the large initial-boundary disturbance by using of the L2 - energy method.

关 键 词：广义BBM-BURGERS方程 一般初边值问题 大扰动 L2-能量方法 

分 类 号：O175.27[理学—数学]