A new approach to the inverse discrete transmission eigenvalue problem

Bondarenko Natalia P.; Yurko Vjacheslav A.

doi:10.3934/ipi.2021073

Article Contents

2022, Volume 16, Issue 4: 739-751. Doi: 10.3934/ipi.2021073

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A new approach to the inverse discrete transmission eigenvalue problem

Bondarenko Natalia P.^1,2, , and
Yurko Vjacheslav A.^2,

1.
Department of Applied Mathematics and Physics, Samara National Research University, Moskovskoye Shosse 34, Samara 443086, Russia
2.
Department of Mechanics and Mathematics, Saratov State University, Astrakhanskaya 83, Saratov 410012, Russia

^*Corresponding author: Natalia P. Bondarenko
^*Corresponding author: Natalia P. Bondarenko

Received: May 31, 2021

Revised: August 31, 2021

Early access: December 2021

Published: August 2022

The authors are supported by RFBR grants 20-31-70005, 19-01-00102

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Abstract

A discrete analog is considered for the inverse transmission eigenvalue problem, having applications in acoustics. We provide a well-posed inverse problem statement, develop a constructive procedure for solving this problem, prove uniqueness of solution, global solvability, local solvability, and stability. Our approach is based on the reduction of the discrete transmission eigenvalue problem to a linear system with polynomials of the spectral parameter in the boundary condition.

Keywords:

Inverse problems,
discrete transmission eigenvalue problem,
Weyl function,
global solvability,
local solvability,
stability.

Mathematics Subject Classification: Primary: 15A29; Secondary: 15A18, 34A55.

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References

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