论文标题
降低对数类型演化方程：渐近概况和最佳估计值
A dissiptive logarithmic type evolution equation: asymptotic profile and optimal estimates
论文作者
论文摘要
我们介绍了一种具有非局部对数阻尼机制的对数类型的波形样式的新模型，与经常研究的分数阻尼病例相比，该模型相当有效。我们考虑了整个空间中这个新模型的库奇问题，并研究了解决方案的渐近曲线和最佳衰减和/或爆炸速率，因为时间流向了l^{2} - sense中的无穷大。本文中考虑的操作员l用于消除Charao-ikehata在2020年研究的论文中的波动方程的溶液，在低频参数中，方程式的主要部分和阻尼项的有效性比备受良好的电力类型运算符相当弱。
We introduce a new model of the logarithmic type of wave-like equation with a nonlocal logarithmic damping mechanism, which is rather weakly effective as compared with frequently studied fractional damping cases. We consider the Cauchy problem for this new model in the whole space, and study the asymptotic profile and optimal decay and/or blowup rates of solutions as time goes to infinity in L^{2}-sense. The operator L considered in this paper was used to dissipate the solutions of the wave equation in the paper studied by Charao-Ikehata in 2020, and in the low frequency parameters the principal part of the equation and the damping term is rather weakly effective than those of well-studied power type operators.
