The Transmission Eigenvalue Problem of Exterior Inverse Scattering in Fully Coated Inhomogeneous Media

DING Hui; LIU Lihan

doi:10.21656/1000-0887.450207

Volume 46 Issue 6

Jun. 2025

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DING Hui, LIU Lihan. The Transmission Eigenvalue Problem of Exterior Inverse Scattering in Fully Coated Inhomogeneous Media[J]. Applied Mathematics and Mechanics, 2025, 46(6): 781-790. doi: 10.21656/1000-0887.450207

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The Transmission Eigenvalue Problem of Exterior Inverse Scattering in Fully Coated Inhomogeneous Media

doi: 10.21656/1000-0887.450207

DING Hui,
LIU Lihan^,

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

Received Date: 2024-07-12
Rev Recd Date: 2024-09-03
Publish Date: 2025-06-01

Abstract

Abstract

The transmission eigenvalue problem of exterior inverse scattering in fully coated inhomogeneous media was studied. Firstly, a nonlinear 4th-order formulation was established based on the classical process, and the existence and discreteness were proved by the Lax-Milgram theorem and the Fredholm theory. Next, by means of an equivalent mixed formulation with an auxiliary variable, the problem is transformed into a linear eigenvalue problem, and an appropriate operator was constructed by the Riesz representation theorem and the Rellich-Kondrachov compactness theorem, etc. The compactness and coerciveness of the operators were proved with the Cauchy convergence criterion, the Brezzi theory and the Poincaré inequality.
- fully coated boundary,
- exterior inverse scattering,
- transmission eigenvalue

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References

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