Transmission Eigenvalues for Helmholtz Equation Perturbation Problems of Isotropic Media With Voids
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摘要: 传输特征值在反散射唯一性理论中具有十分重要的意义.在含空隙的各向同性非均匀介质折射率扰动下，研究了Helmholtz方程传输特征值的存在性问题.首先，通过构造Neumann-Dirichlet算子，建立传输特征值问题的等价形式.然后，进一步构造特征值函数，将扰动的传输特征值问题转化为算子为零特征值的扰动问题.最后，利用隐函数定理的扰动方法证明传输特征值的存在性.
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关键词:
- 扰动 /
- 传输特征值 /
- Neumann-Dirichlet算子 /
- Helmholtz方程
Abstract: Transmission eigenvalues are of major interests in the inverse scattering theory for uniqueness. For the Helmholtz equation of isotropic inhomogeneous media with voids, the existence of transmission eigenvalues was studied for the Helmholtz equation under the refractive index perturbation of the media. Firstly, through construction of the Neumann-Dirichlet operator, the equivalent form of the transmission eigenvalue problem was obtained. Then, the eigenvalue function was built to transform the perturbation problem for transmission eigenvalues into the perturbation problem for zero eigenvalues of operators. Finally, the perturbation method based on the implicit function theorem was used to prove the existence of transmission eigenvalues.-
Key words:
- perturbation /
- transmission eigenvalue /
- Neumann-Dirichlet operator /
- Helmholtz equation
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