论文标题
关于复杂值内部传输特征值的轨迹
On trajectories of complex-valued interior transmission eigenvalues
论文作者
论文摘要
本文研究了由均匀介质的折射索引参数参数参数的内部传播问题的复合价值特征值轨迹的特性。我们对单位磁盘的理论分析表明，与真实轴的唯一相交点，以及随着折射率倾向于无穷大的唯一轨迹限制点，是Laplacian的Dirichlet特征值。补充数值实验甚至会产生Laplacian的Dirichlet特征值和复杂值内部传输特征值轨迹之间的一对一对应关系。我们还检查了可以进行类似数值观察的磁盘以外的其他散射器。我们将结果总结为一般简单连接的散点子的猜想。
This paper investigates properties of complex-valued eigenvalue trajectories for the interior transmission problem parametrized by the index of refraction for homogeneous media. Our theoretical analysis for the unit disk shows that the only intersection points with the real axis, as well as the unique trajectorial limit points as the refractive index tends to infinity, are Dirichlet eigenvalues of the Laplacian. Complementing numerical experiments even give rise to an underlying one-to-one correspondence between Dirichlet eigenvalues of the Laplacian and complex-valued interior transmission eigenvalue trajectories. We also examine other scatterers than the disk for which similar numerical observations can be made. We summarize our results in a conjecture for general simply-connected scatterers.
