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On the energy decay rate of the fractional wave equation on ℝ with relatively dense damping
Proceedings of the American Mathematical Society ( IF 0.8 ) Pub Date : 2020-08-11 , DOI: 10.1090/proc/15100 Walton Green
Proceedings of the American Mathematical Society ( IF 0.8 ) Pub Date : 2020-08-11 , DOI: 10.1090/proc/15100 Walton Green
Abstract:We establish upper bounds for the decay rate of the energy of the damped fractional wave equation when the averages of the damping coefficient on all intervals of a fixed length are bounded below. If the power of the fractional Laplacian, 
, is between 0 and 2, the decay is polynomial. For 
, the decay is exponential. Our assumption is also necessary for energy decay. Second, we prove that exponential decay cannot hold for 
if the damping vanishes at all.
中文翻译：
阻尼比较大的ℝ上分数阶波动方程的能量衰减率
摘要：在固定长度的所有区间上的阻尼系数平均值均在以下范围内时，我们为阻尼分数波方程的能量衰减率设定了上限。如果分数拉普拉斯算子的幂在0和2之间，则衰减为多项式。对于，衰减是指数的。我们的假设对于能量衰减也是必要的。其次，我们证明，如果阻尼消失，指数衰减就无法成立。
更新日期：2020-09-02
, is between 0 and 2, the decay is polynomial. For , the decay is exponential. Our assumption is also necessary for energy decay. Second, we prove that exponential decay cannot hold for if the damping vanishes at all. 中文翻译：
阻尼比较大的ℝ上分数阶波动方程的能量衰减率
摘要：在固定长度的所有区间上的阻尼系数平均值均在以下范围内时，我们为阻尼分数波方程的能量衰减率设定了上限。如果分数拉普拉斯算子的幂
在0和2之间，则衰减为多项式。对于，衰减是指数的。我们的假设对于能量衰减也是必要的。其次，我们证明，如果阻尼消失，指数衰减就无法成立。
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