广义Kdv-Burgers方程的初边值问题
The Initial and Boundary Value Problem to the Generalized Kdv-Burgers Equation
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。
Abstract: 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.
文章引用：张洁. 广义Kdv-Burgers方程的初边值问题[J]. 应用数学进展, 2022, 11(10): 7067-7078. https://doi.org/10.12677/AAM.2022.1110750

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