大扰动下非凸广义BBM-Burgers方程解的渐近性态(上)  

Asymptotic behaviors of solutions for generalized BBM-Burgers equation with non-convexity and large initial disturbance(Ⅰ)

作　　者：陈诚[1] 

机构地区：[1]暨南大学数学系,广州510632

出　　处：《哈尔滨商业大学学报（自然科学版）》2013年第1期125-128,共4页Journal of Harbin University of Commerce：Natural Sciences 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,其边界条件为u(0,t)=u-(t)→u-(t→∞),初始值u(x,0)=u0(x)→u+(x→∞),u0(0)=u-(0),u±是给定的常数且满足u-<0<u+,|u+-u-|为充分小的正数.在流函数f为非凸及初始值为大扰动条件下,利用L2加权能量方法证明相应初边值问题解的整体存在性及渐近收敛于弱稳定波和弱稀疏波的线性叠加.This paper is concerned with the initial -boundary value problem for the general- ized BBM -Burgers equation ut ＋f（u） x = Uxx ＋ Uxx, with the general boundary condition u（0, t） =u （0） = small. _ （t）→u_ （t→∞and the initial date satisfying u（x,O） = U0（X）→u＋ （x→∞）,u= u0 （0）, where u ± were given constants, u _ 〈 0 〈 u ＋ and ｜ u ＋ - u_ ｜ was sufficiently Under the condition that the flux function f was not convex, it was proved that the global solution of corresponding general initial - boundary value problem exists and converges time -asymptotically to the linear superposition of a weak stationary wave and a weak rare- faction wave for the large initial disturbance by using of an L2 weighted energy method.

关 键 词：广义BBM—Burgers方程 一般初边值问题 大扰动 非凸条件 L^2加权能量方法 

分 类 号：O175.27[理学—数学]