论文标题
带有奇异阻尼的阻尼波方程
The damped wave equation with singular damping
论文作者
论文摘要
我们在有限的间隔内分析了$α/x $，$α> 0 $的单数阻尼，分析了阻尼波方程的溶液的光谱特性和特殊行为。我们为所有正$α$建立了半群的指数稳定性，并确定频谱的条件由有限数量的特征值组成。结果，我们充分表征了在有限时间内灭绝解决方案的一组初始条件。最后，我们提出了两个与极端衰减率有关的开放问题。
We analyze the spectral properties and peculiar behavior of solutions of a damped wave equation on a finite interval with a singular damping of the form $α/x$, $α>0$. We establish the exponential stability of the semigroup for all positive $α$, and determine conditions for the spectrum to consist of a finite number of eigenvalues. As a consequence, we fully characterize the set of initial conditions for which there is extinction of solutions in finite time. Finally, we propose two open problems related to extremal decay rates of solutions.
