广义BBM-Burgers方程扩散波的初边值问题
Initial Boundary Value Problem of Diffused Waves in Generalized BBM-Burgers Equation
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。
Abstract: 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.
文章引用：刘媛媛. 广义BBM-Burgers方程扩散波的初边值问题[J]. 理论数学, 2024, 14(4): 240-249. https://doi.org/10.12677/PM.2024.144131

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