论文标题
与对数阻尼的某些波动方程的溶液的渐近曲线和最佳衰变
Asymptotic profile and optimal decay of solutions of some wave equations with logarithmic damping
论文作者
论文摘要
我们引入了具有对数阻尼机制的非本地波方程的新模型。我们考虑了整个空间中新型号的Cauchy Poroblem。随着时间的流逝，我们研究了解决方案的渐近概况，最佳衰减和爆炸速率。到目前为止，尚未研究本文中考虑的缩放术语，在低频参数中，阻尼比研究精心局部的非本地阻尼的术语相当弱。为了获得最佳估计，我们符合具有特殊参数的所谓超几何函数。
We introduce a new model of the nonlocal wave equations with a logarithmic damping mechanism. We consider the Cauchy poroblem for the new model in the whole space. We study the asymptotic profile and optimal decay and blowup rates of solutions as time goes to infinity. The damping terms considered in this paper is not studied so far, and in the low frequency parameters the damping is rather weakly effective than that of well-studied fractional type of nonlocal damping. In order to get the optimal estimates in time we meet the so-called hypergeometric functions with special parameters.
