摘要
本文主要研究的是广义BBM-Burgers方程的初边值问题,利用能量估计的方法证明了广义BBM-Burgers方程的解关于扩散波的渐近稳定性。即对方程:在本文中我们将证明在波的强度及初值u0(x)适当小的情况下,广义BBM-Burgers方程的解整体存在且当时间t趋于无穷时收敛到非线性扩散波。
This paper studies the initial boundary value problem of the generalized BBM-Burgers equation, and proves the asymptotic stability of the solution of the generalized BBM-Burgers equation with respect to the diffusion wave by using the method of energy estimation. To the equation: , in this paper, we will prove that the solution of the generalized BBM-Burgers equation exists as a whole and converges to the nonlinear diffusion waveas time t approaches infinity when the wave intensityand initial value u0(x) are appropriately small.
出处
《理论数学》
2024年第4期240-249,共10页
Pure Mathematics
