论文标题
波动方程的频谱在非紧密恒星图上具有狄拉克阻尼的频谱
Spectrum of the wave equation with Dirac damping on a non-compact star graph
论文作者
论文摘要
我们考虑在非紧密恒星图上的波方程，受到通过具有复杂耦合的罗宾型顶点条件定义的分布阻尼。结果表明，进化问题的非自动选择发生器承认其光谱属性突然变化，以与图形边数相关的特殊耦合。作为应用程序，我们表明进化问题对于关键耦合非常不稳定。还提到了与非相关量子力学中狄拉克方程的关系。
We consider the wave equation on non-compact star graphs, subject to a distributional damping defined through a Robin-type vertex condition with complex coupling. It is shown that the non-self-adjoint generator of the evolution problem admits an abrupt change in its spectral properties for a special coupling related to the number of graph edges. As an application, we show that the evolution problem is highly unstable for the critical couplings. The relationship with the Dirac equation in non-relativistic quantum mechanics is also mentioned.
