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Asymptotic stability of diffusion wave for a semilinear wave equation with damping
Journal of Mathematical Analysis and Applications ( IF 1.2 ) Pub Date : 2021-07-05 , DOI: 10.1016/j.jmaa.2021.125468 Yan Yong 1 , Junmei Su 1
中文翻译:
带阻尼半线性波动方程的扩散波渐近稳定性
更新日期:2021-08-30
Journal of Mathematical Analysis and Applications ( IF 1.2 ) Pub Date : 2021-07-05 , DOI: 10.1016/j.jmaa.2021.125468 Yan Yong 1 , Junmei Su 1
Affiliation
This paper studies the asymptotic behavior of the solution to the Cauchy problem of a semilinear wave equation with damping , , under some smallness conditions. By applying elementary energy method, we prove the solution of the above equation tends to the planar diffusion wave time-asymptotically, where is a self-similar solution of the one dimensional equation , with . In addition, this paper gives the time decay rate, namely, , where .
中文翻译:
带阻尼半线性波动方程的扩散波渐近稳定性
本文研究了具有阻尼的半线性波动方程柯西问题解的渐近行为 , ,在一些小的条件下。应用初等能量法,证明上述方程的解趋于平面扩散波 时间渐近,其中 是一维方程的自相似解 , 和 . 此外,本文给出了 时间衰减率,即 , 在哪里 .