论文标题
临界对数阻尼的波方程的L^2-Norm的渐近谱
Asymptotic profile of L^2-norm of solutions for wave equations with critical log-damping
论文作者
论文摘要
我们考虑具有特殊类型的对数划分阻尼的波浪方程。我们在整个空间中研究了该模型的Cauchy问题，并且随着时间的流逝，我们获得了渐近的概况和最佳溶液估计值，以l^2-Sense的无穷大。该注释的最大发现是，在有效阻尼下，如果n = 1 l^2-norm在无限的时间内爆炸，而在溶液的n = 2 l^2-norm中，溶液的溶液永远不会腐烂，并且在无限时间内永远不会爆炸。后一种现象似乎是一个罕见的情况。
We consider wave equations with a special type of log-fractional damping. We study the Cauchy problem for this model in the whole space, and we obtain an asymptotic profile and optimal estimates of solutions as time goes to infinity in L^2-sense. A maximal discovery of this note is that under the effective damping, in case of n = 1 L^2-norm of the solution blows up in infinite time, and in case of n = 2 L^2-norm of the solution never decays and never blows up in infinite time. The latter phenomenon seems to be a rare case.
