Asymptotic profile of solutions for semilinear wave equations with structural damping
Asymptotic profile of solutions for semilinear wave equations with structural damping
复制标题
具有结构阻尼的半线性波动方程解的渐近轮廓
DOI：
10.1007/s00030-019-0562-x
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
Taeko Yamazaki
中科院分区：
文献类型：
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作者：
Ikehata;M. and Kawashita;M.;Tetsutaro Shibata;Taeko Yamazaki
研究具有结构阻尼的半线性波动方程的初值问题。我们首先证明了在（）上的一些加权Sobolev空间中初始数据小的全局存在性。接下来，我们证明了上述解的渐近轮廓是由相应抛物方程的基本解的常数倍给出的，假设初始数据属于加权空间。
This paper is concerned with the initial value problem for semilinear wave equation with structural damping, whereandorwith. We first show the global existence for initial data small in some weighted Sobolev spaces on(). Next, we show that the asymptotic profile of the solution above is given by a constant multiple of the fundamental solution of the corresponding parabolic equation, provided the initial data belong to weightedspaces.