Transmission Eigenvalues for Helmholtz Equation Perturbation Problems of Isotropic Media With Voids

LI Shixuan; LIU Lihan

doi:10.21656/1000-0887.440221

Volume 44 Issue 11

Nov. 2023

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LI Shixuan, LIU Lihan. Transmission Eigenvalues for Helmholtz Equation Perturbation Problems of Isotropic Media With Voids[J]. Applied Mathematics and Mechanics, 2023, 44(11): 1389-1397. doi: 10.21656/1000-0887.440221

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Transmission Eigenvalues for Helmholtz Equation Perturbation Problems of Isotropic Media With Voids

doi: 10.21656/1000-0887.440221

LI Shixuan,
LIU Lihan^,

School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, P.R.China

Received Date: 2023-07-18
Rev Recd Date: 2023-09-05
Publish Date: 2023-11-01

Abstract

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.
- perturbation,
- transmission eigenvalue,
- Neumann-Dirichlet operator,
- Helmholtz equation

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References(23)

References

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