Thresholds for low regularity solutions to wave equation with structural damping
Thresholds for low regularity solutions to wave equation with structural damping
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具有结构阻尼的波动方程低正则解的阈值
DOI：
10.1016/j.jmaa.2020.124669
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发表时间：
2021
期刊：
影响因子：
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通讯作者：
Ryo Ikehata
中科院分区：
文献类型：
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作者：
Tomonori Fukushima;Hironori Michihisa;Ryo Ikehata
研究了具有结构阻尼项ut-Δ u+ Δ 2 ut = 0，u（0，x）= u 0（x），ut（0，x）= u1（x）的波动方程解在全空间的渐近性态.本文报道了新的阈值，表明其中的扩散波属性和非扩散结构占主导地位，在低的规则性的情况下。为此，我们发展了以前作者的研究[2]，他们提出了一个阈值，表示是否抛物线状的性质或波动性质强烈出现在一些规则性损失型耗散波方程的解决方案。
We study the asymptotic behavior of solutions to wave equations with the structural damping term u t t− Δ u+ Δ 2 u t= 0, u (0, x)= u 0 (x), u t (0, x)= u 1 (x), in the whole space. New thresholds are reported in this paper that indicate which of the diffusion wave property and the non-diffusive structure dominates in low regularity cases. We develop to that end the previous authors' research [2] where they have proposed a threshold that expresses whether the parabolic-like property or the wave-like property strongly appears in the solution to some regularity-loss type dissipative wave equation.