Large time behavior of solutions to elastic wave with structural damping
Large time behavior of solutions to elastic wave with structural damping
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DOI：
10.1016/j.jde.2022.04.017
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发表时间：
2022-07
影响因子：
2.4
通讯作者：
H. Takeda
中科院分区：
文献类型：
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作者：
H. Takeda
在本文中，我们考虑具有结构阻尼项的弹性波的柯西问题。基于我们之前的工作[10]，我们获得了解 u 当 t→∞ 时的渐近轮廓。也就是说，我们证明了特殊函数解的近似公式，这表明 u 的渐近轮廓根据方程中的参数分为几种模式。因此，我们得出 u 范数的下界，这意味着 [1]、[3]、[8]、[18] 中的时间衰减估计对于大 t 来说是尖锐的。
In this paper, we consider the Cauchy problem for elastic waves with structural damping term. Based on our previous work [10], we obtain asymptotic profiles of solutions u as t→∞. Namely, we prove approximation formulas of the solutions by the special functions, which shows the asymptotic profiles of u are classified into several patterns, depending on the parameter in the equation. As a consequence, we conclude the lower bound of the norms of u, which implies time decay estimates in [1],[3],[8],[18] are sharp for large t.