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Pure Mathematics 2024
广义BBM-Burgers方程初边值问题的L2衰减估计
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Abstract:
本文主要研究如下本文研究的是广义BBM-Burgers方程扩散波的衰减估计问题，利用已经证明过的广义BBM-Burgers方程的解关于扩散波的渐近稳定，对该解进行衰减估计，并且在本文将证明广义BBM-Burgers方程解在L2范数下的衰减速度为(1t)？12。即对方程：{utf(u)x=uxxuxxtu(x,t)|t=0=u0(x),u(0,t)=u？在本文中我们将证明在波的强度δ:=|u？u？|及初值u0(x)适当小的情况下，广义BBM-Burgers方程的扰动方程形式的解的衰减速度为(1t)？12。
This paper mainly studies as follows: This paper studies the attenuation estimation of the diffusion wave of the generalized BBM-Burgers equation. The solution of the generalized BBM-Burgers equation, which has been proved to be about the asymptotic stability of the diffusion wave, is used to estimate the attenuation of the solution. In this paper, it is proved that the decay rate of the solution of the generalized BBM-Burgers equation is(1t)？12under the L2 norm. Immediate pair equation:{utf(u)x=uxxuxxtu(x,t)|t=0=u0(x),u(0,t)=u？in this paper, we will prove that if the wave intensityδ:=|u？u？|and the initial valueu0(x)are appropriately small, the decay velocity of the perturbation equation of the generalized BBM-Burgers equation is(1t)？12.
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