scholarly journals A Uniqueness Theorem for Bessel Operator from Interior Spectral Data

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Murat Sat ◽  
Etibar S. Panakhov
Keyword(s):  
Inverse Problem ◽  
Uniqueness Theorem ◽  
Spectral Data ◽  
Bessel Operator ◽  
Uniqueness Theorems ◽  
Internal Point

Inverse problem for the Bessel operator is studied. A set of values of eigenfunctions at some internal point and parts of two spectra are taken as data. Uniqueness theorems are obtained. The approach that was used in investigation of problems with partially known potential is employed.

Determination of an impulsive diffusion operator from interior spectral data

Analysis ◽  
2020 ◽  
Vol 40 (1) ◽  
pp. 39-45
Author(s):  
Yasser Khalili ◽  
Dumitru Baleanu
Keyword(s):  
Inverse Problem ◽  
Spectral Data ◽  
Potential Functions ◽  
Half Line ◽  
Internal Point ◽  
Diffusion Operator ◽  
Impulsive Diffusion

AbstractIn the present work, the interior spectral data is used to investigate the inverse problem for a diffusion operator with an impulse on the half line. We show that the potential functions {q_{0}(x)} and {q_{1}(x)} can be uniquely established by taking a set of values of the eigenfunctions at some internal point and one spectrum.

A uniqueness result for differential pencils with discontinuities from interior spectral data

Analysis ◽  
2019 ◽  
Vol 38 (4) ◽  
pp. 195-202
Author(s):  
Yasser Khalili ◽  
Dumitru Baleanu
Keyword(s):  
Inverse Problem ◽  
Spectral Data ◽  
Uniqueness Result ◽  
Half Line ◽  
Internal Point ◽  
Diffusion Operator ◽  
Differential Pencils

Abstract In this work, the interior spectral data is employed to study the inverse problem for a differential pencil with a discontinuity on the half line. By using a set of values of the eigenfunctions at some internal point and eigenvalues, we obtain the functions {q_{0}(x)} and {q_{1}(x)} applied in the diffusion operator.

scholarly journals Recovering differential pencils with spectral boundary conditions and spectral jump conditions

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Yasser Khalili ◽  
Dumitru Baleanu
Keyword(s):  
Boundary Condition ◽  
Inverse Problem ◽  
Boundary Conditions ◽  
Spectral Parameter ◽  
Second Order ◽  
Uniqueness Theorems ◽  
Jump Conditions ◽  
Internal Point ◽  
Differential Pencils

AbstractIn this work, we discuss the inverse problem for second order differential pencils with boundary and jump conditions dependent on the spectral parameter. We establish the following uniqueness theorems: $(i)$ ( i ) the potentials $q_{k}(x)$ q k ( x ) and boundary conditions of such a problem can be uniquely established by some information on eigenfunctions at some internal point $b\in (\frac{\pi }{2},\pi )$ b ∈ ( π 2 , π ) and parts of two spectra; $(ii)$ ( i i ) if one boundary condition and the potentials $q_{k}(x)$ q k ( x ) are prescribed on the interval $[\pi /2(1-\alpha ),\pi ]$ [ π / 2 ( 1 − α ) , π ] for some $\alpha \in (0, 1)$ α ∈ ( 0 , 1 ) , then parts of spectra $S\subseteq \sigma (L)$ S ⊆ σ ( L ) are enough to determine the potentials $q_{k}(x)$ q k ( x ) on the whole interval $[0, \pi ]$ [ 0 , π ] and another boundary condition.

scholarly journals Inverse problem for fractional diffusion equation

2011 ◽  
Vol 14 (1) ◽  
Author(s):  
Vu Tuan
Keyword(s):  
Inverse Problem ◽  
Diffusion Coefficient ◽  
Lower Bound ◽  
Diffusion Equation ◽  
Spectral Data ◽  
A Priori ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
One Dimensional ◽  
Initial Distributions

AbstractWe prove that by taking suitable initial distributions only finitely many measurements on the boundary are required to recover uniquely the diffusion coefficient of a one dimensional fractional diffusion equation. If a lower bound on the diffusion coefficient is known a priori then even only two measurements are sufficient. The technique is based on possibility of extracting the full boundary spectral data from special lateral measurements.

scholarly journals Recovering singular differential operators on noncompact star-type graphs from Weyl functions

2011 ◽  
Vol 42 (2) ◽  
pp. 223-236
Author(s):  
V. Yurko
Keyword(s):  
Inverse Problem ◽  
Uniqueness Theorem ◽  
Differential Operators ◽  
Spectral Characteristics ◽  
Method Of Spectral Mappings ◽  
Weyl Functions

Bessel-type differential operators on noncompact star-type graphs are studied. We establish properties of the spectral characteristics and then we investigate the inverse problem of recovering the operator from the so-called Weyl vector. For this inverse problem we prove a uniqueness theorem and propose a procedure for constructing the solution using the method of spectral mappings.

scholarly journals An interior inverse problem for the impulsive Dirac operator

2011 ◽  
Vol 42 (3) ◽  
pp. 259-263 ◽  
Author(s):  
Sinan Özkan ◽  
Rauf Kh. Amirov
Keyword(s):  
Inverse Problem ◽  
Dirac Operator ◽  
Potential Function ◽  
Differential Operators ◽  
Internal Point

In this study, an inverse problem for Dirac differential operators with discontinuities is studied. It is shown that the potential function can be uniquely determined by a set of values of eigenfunctions at some internal point and one spectrum.

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.

An Inverse Problem of Eigenvalue for Generalized Anti-Tridiagonal Matrices

2012 ◽  
Vol 424-425 ◽  
pp. 377-380
Author(s):  
Hui Wang ◽  
Zhi Bin Li
Keyword(s):  
Inverse Problem ◽  
Inverse Problems ◽  
Uniqueness Theorem ◽  
Numerical Example ◽  
Tridiagonal Matrices

An inverse problem of eigenvalue for generalized Anti-Tridiagonal Matrices is discussed on the base of some inverse problems of Eigenvalue for Anti-Tridiagonal Matrices. The algorithm and uniqueness theorem of the solution of the problem are given, and some numerical example is provided

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