广义Kdv-Burgers方程的初边值问题  

The Initial and Boundary Value Problem to the Generalized Kdv-Burgers Equation

作　　者：张洁[1] 

机构地区：[1]上海理工大学,上海

出　　处：《应用数学进展》2022年第10期7067-7078,共12页Advances in Applied Mathematics

摘　　要：本文研究了广义Kdv-burgers方程的初边值问题,说明了广义Kdv-burgers方程的解关于扩散波的渐近稳定性。即对方程: ,我们证明了在一些小性条件下,广义Kdv-burgers方程的解整体存在且当时间t趋于无穷时收敛到扩散波。In this paper, we studied the initial and boundary value problem to the generalized KdV-Burgers equation;we will show the large time asymptotic stability of diffusion waves to the problem i.e. for the equation: . It’s proved that under some smallness conditions the solution of the generalized Kdv-burgers equation exists globally and converges to the diffusion wave when the time t tends to infinity.

关 键 词：广义KDV-BURGERS方程 初边值问题 能量方法 扩散波 衰减速度 

分 类 号：O175.8[理学—数学]