We study a nonlocal wave equation with logarithmic damping, which is rather weak in the low-frequency zone as compared with frequently studied strong damping case. We consider the Cauchy problem for this model in Rⁿ, and we study the asymptotic profile and optimal estimates of the solutions and the total energy as t → ∞ in L² sense. In that case, some results on hypergeometric functions are useful.

中文翻译：

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具有参数相关对数阻尼的波动方程的渐近轮廓

我们研究了一个具有对数阻尼的非局部波动方程，与经常研究的强阻尼情况相比，它在低频区相当弱。我们在R ^{n 中}考虑该模型的柯西问题，并且我们研究了在L ²意义上的解和总能量的渐近分布和最优估计值t  →  ∞。在这种情况下，超几何函数的一些结果是有用的。