Diffusion phenomena for the wave equation with space-dependent damping in an exterior domain

Diffusion phenomena for the wave equation with space-dependent damping in an exterior domain
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外部域中具有空间相关阻尼的波动方程的扩散现象

DOI：
10.1016/j.jde.2016.08.006
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发表时间：
2016
期刊：
J. Differential Equations
影响因子：
--
通讯作者：
M. Sobajima and Y. Wakasugi
M. Sobajima and Y. Wakasugi
中科院分区：
--
文献类型：
--
作者：
Giorgio Metafune;Motohiro Sobajima;Chiara Spina;M. Sobajima and Y. Wakasugi;M. Sobajima and Y. Wakasugi

文献摘要

相似文献

在这篇文章中，我们考虑了具有空间相关阻尼项的波动方程在外部区域中解的渐近行为。我们证明了当阻尼有效时，当时间趋于无穷大时，解被相应的热方程的解近似。我们的证明基于相应热方程的半群估计和阻尼波方程的加权能量估计。文中还建立了迟解衰变的最优性。
In this paper, we consider the asymptotic behavior of solutions to the wave equation with space-dependent damping in an exterior domain. We prove that when the damping is effective, the solution is approximated by that of the corresponding heat equation as time tends to infinity. Our proof is based on semigroup estimates for the corresponding heat equation and weighted energy estimates for the damped wave equation. The optimality of the decay late for solutions is also established.