scholarly journals The uniqueness in the inverse problem for transmission eigenvalues for the spherically symmetric variable-speed wave equation

2011 ◽  
Vol 27 (11) ◽  
pp. 115004 ◽  
Author(s):  
Tuncay Aktosun ◽  
Drossos Gintides ◽  
Vassilis G Papanicolaou
Keyword(s):  
Inverse Problem ◽  
Wave Equation ◽  
Spherically Symmetric ◽  
Variable Speed ◽  
Transmission Eigenvalues ◽  
Symmetric Variable

Isospectral sets for transmission eigenvalue problem

2020 ◽  
Vol 28 (1) ◽  
pp. 63-69 ◽  
Author(s):  
Chuan-Fu Yang ◽  
Sergey A. Buterin
Keyword(s):  
Wave Equation ◽  
Eigenvalue Problem ◽  
Wave Speed ◽  
Spherically Symmetric ◽  
Variable Speed ◽  
Transmission Eigenvalues ◽  
Constructive Methods ◽  
Transmission Eigenvalue ◽  
Symmetric Variable ◽  
Transmission Eigenvalue Problem

AbstractWe consider the boundary value problem {R(a,q)}: {-y^{\prime\prime}(x)+q(x)y(x)=\lambda y(x)} with {y(0)=0} and {y(1)\cos(a\sqrt{\lambda})=y^{\prime}(1)\frac{\sin(a\sqrt{\lambda})}{\sqrt{% \lambda}}}. Motivated by the previous work [T. Aktosun and V. G. Papanicolaou, Reconstruction of the wave speed from transmission eigenvalues for the spherically symmetric variable-speed wave equation, Inverse Problems 29 2013, 6, Article ID 065007], it is natural to consider the following interesting question: how does one characterize isospectral sets corresponding to problem {R(1,q)}? In this paper applying constructive methods we answer the above question.

The interior transmission eigenvalue problem for a spherically-symmetric domain with anisotropic medium and a cavity

2015 ◽  
Vol 23 (4) ◽  
Author(s):  
Andreas Kirsch ◽  
Hayk Asatryan
Keyword(s):  
Inverse Problem ◽  
Anisotropic Medium ◽  
Acoustic Waves ◽  
Symmetric Domain ◽  
Spherically Symmetric ◽  
Scattering Problems ◽  
Transmission Eigenvalues ◽  
Transmission Eigenvalue ◽  
Transmission Eigenvalue Problem ◽  
Infinite Set

AbstractWe consider the scattering of spherically-symmetric acoustic waves by an anisotropic medium and a cavity. While there is a large number of recent works devoted to the scattering problems with cavities, existence of an infinite set of transmission eigenvalues is an open problem in general. In this paper we prove existence of an infinite set of transmission eigenvalues for anisotropic Helmholtz and Schrödinger equations in a spherically-symmetric domain with a cavity. Further in this paper we consider the corresponding inverse problem. Under some assumptions we prove the uniqueness in the inverse problem.

scholarly journals Discrete regularization and convergence of the inverse problem for 1+1 dimensional wave equation

2019 ◽  
Vol 13 (3) ◽  
pp. 575-596 ◽  
Author(s):  
Jussi Korpela ◽  
◽  
Matti Lassas ◽  
Lauri Oksanen ◽  
Keyword(s):  
Inverse Problem ◽  
Wave Equation ◽  
Dimensional Wave

Inverse problem for one-dimensional wave equation with matrix potential

2019 ◽  
Vol 27 (2) ◽  
pp. 217-223 ◽  
Author(s):  
Ammar Khanfer ◽  
Alexander Bukhgeim
Keyword(s):  
Inverse Problem ◽  
Wave Equation ◽  
Uniqueness Theorem ◽  
Cauchy Data ◽  
Global Uniqueness ◽  
One Dimensional ◽  
Matrix Potential ◽  
The Matrix ◽  
Real Matrices ◽  
Dimensional Wave

AbstractWe prove a global uniqueness theorem of reconstruction of a matrix-potential {a(x,t)} of one-dimensional wave equation {\square u+au=0}, {x>0,t>0}, {\square=\partial_{t}^{2}-\partial_{x}^{2}} with zero Cauchy data for {t=0} and given Cauchy data for {x=0}, {u(0,t)=0}, {u_{x}(0,t)=g(t)}. Here {u,a,f}, and g are {n\times n} smooth real matrices, {\det(f(0))\neq 0}, and the matrix {\partial_{t}a} is known.

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