Inverse spectral problems of transmission eigenvalue problem for anisotropic media with spherical symmetry assumptions

2017 ◽  
Vol 25 (2) ◽  
Author(s):  
Xiao-Chuan Xu ◽  
Chuan-Fu Yang ◽  
Sergey A. Buterin
Keyword(s):  
Eigenvalue Problem ◽  
Boundary Conditions ◽  
Spectral Problem ◽  
Anisotropic Medium ◽  
Spherical Symmetry ◽  
Inverse Spectral Problem ◽  
Inverse Spectral Problems ◽  
Transmission Eigenvalue ◽  
Transmission Eigenvalue Problem ◽  
Inverse Spectral

Abstract We investigate the inverse spectral problem of the interior transmission eigenvalue problem for an anisotropic medium supported in with the boundary conditions

scholarly journals Inverse spectral boundary problem Sturm Liouville type with constant delay and non-zero initial function

2021 ◽  
Vol 51 ◽  
pp. 18-30
Author(s):  
Milenko Pikula ◽  
Dragana Nedić ◽  
Ismet Kalco ◽  
Ljiljanka Kvesić
Keyword(s):  
Boundary Conditions ◽  
Spectral Problem ◽  
Boundary Problem ◽  
Initial Function ◽  
Inverse Spectral Problem ◽  
Constant Delay ◽  
Liouville Type ◽  
Sturm Liouville ◽  
Inverse Spectral ◽  
The Right

This paper is dedicated to solving of the direct and inverse spectral problem for Sturm Liouville type of operator with constant delay from 𝜋/2 to 𝜋, non-zero initial function and Robin’s boundary conditions. It has been proved that two series of eigenvalues unambiguously define the following parameters: delay, coefficients of delay within boundary conditions, the potential on the segment from the point of delay to the right-hand side of the distance and the product of the starting function and potential from the left end of the distance to the delay point.

scholarly journals Inverse spectral problems for differential operators on a graph with a rooted cycle

2009 ◽  
Vol 40 (3) ◽  
pp. 271-286 ◽  
Author(s):  
V. Yurko
Keyword(s):  
Spectral Problem ◽  
Uniqueness Theorem ◽  
Differential Operators ◽  
Inverse Spectral Problem ◽  
Inverse Spectral Problems ◽  
Matching Conditions ◽  
Spectral Problems ◽  
Sturm Liouville ◽  
Inverse Spectral

An inverse spectral problem is studied for Sturm-Liouville differential operators on graphs with a cycle and with standard matching conditions in internal vertices. A uniqueness theorem is proved, and a constructive procedure for the solution is provided.

scholarly journals Solution of a model inverse spectral problem for the Sturm-Liouville operator on a graph

2016 ◽  
pp. 204-211
Author(s):  
Н.Ф. Валеев ◽  
Ю.В. Мартынова ◽  
Я.Т. Султанаев
Keyword(s):  
Boundary Conditions ◽  
Spectral Problem ◽  
Liouville Operator ◽  
Inverse Spectral Problem ◽  
Dimensional Space ◽  
Geometric Graph ◽  
Finite Dimensional Space ◽  
Sturm Liouville ◽  
Inverse Spectral ◽  
Model Inverse

Исследуется модельная обратная спектральная задача для оператора Штурма-Лиувилля на геометрическом графе. Суть данной задачи состоит в восстановлении $N$ параметров граничных условий по $N$ собственным значениям. Установлено, что эта задача обладает свойством монотонной зависимости собственных значений от параметров граничных условий. Поставленная задача сведена к многопараметрической обратной спектральной задаче для оператора в конечномерном пространстве. Предложен новый алгоритм численного решения рассматриваемой задачи. A model inverse spectral problem for the Sturm-Liouville operator on a geometric graph is studied. This problem consists in finding $N$ parameters of the boundary conditions using its $N$ known eigenvalues. It is shown that the problem under consideration possess the property of a monotonic dependence of its eigenvalues on the parameters of the boundary conditions. This problem is reduced to a multiparameter inverse spectral problem for the operator in a finite-dimensional space. A new algorithm for the numerical solution of this problem is proposed.

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