Inverse Problem for a Stieltjes String Damped at an Interior Point

2020 ◽  
Vol 92 (4) ◽  
Author(s):  
Lu Yang ◽  
Yongxia Guo ◽  
Guangsheng Wei
Keyword(s):  
Inverse Problem ◽  
Interior Point ◽  
Stieltjes String

scholarly journals An inverse problem for Sturm-Liouville operators on the half-line having Bessel-type singularity in an interior point

2013 ◽  
Vol 11 (12) ◽  
Author(s):  
Alexey Fedoseev
Keyword(s):  
Inverse Problem ◽  
Interior Point ◽  
Sufficient Conditions ◽  
Weyl Function ◽  
Half Line ◽  
Type Singularity ◽  
Sturm Liouville ◽  
Necessary And Sufficient ◽  
The Given ◽  
Liouville Operators

AbstractWe study the inverse problem of recovering Sturm-Liouville operators on the half-line with a Bessel-type singularity inside the interval from the given Weyl function. The corresponding uniqueness theorem is proved, a constructive procedure for the solution of the inverse problem is provided, also necessary and sufficient conditions for the solvability of the inverse problem are obtained.

Inverse problem for a damped Stieltjes string from parts of spectra

2015 ◽  
Vol 94 (12) ◽  
pp. 2605-2619 ◽  
Author(s):  
Olga Martynuk ◽  
Vyacheslav Pivovarchik ◽  
Christiane Tretter
Keyword(s):  
Inverse Problem ◽  
Stieltjes String

scholarly journals Inverse problems for differential equations on the half-line having a singularity in an interior point

2011 ◽  
Vol 42 (3) ◽  
pp. 343-354 ◽  
Author(s):  
Alexei Fedoseev
Keyword(s):  
Inverse Problem ◽  
Spectral Analysis ◽  
Singular Point ◽  
Inverse Problems ◽  
Uniqueness Theorem ◽  
Interior Point ◽  
Arbitrary Order ◽  
Half Line ◽  
Fundamental Systems ◽  
The Given

Arbitrary order ordinary dierential equations on the half-line having a nonintegrable singularity inside are studied under additional matching conditions for solutions at the singular point. We construct special fundamental systems of solutions for this class of dierential equations, study their asymptotical, analytical and structural properties and the behavior of the corresponding Stokes multipliers. These fundamental systems of solutions are used in spectral analysis of dierential operators with singularities. We study the inverse problem of recovering dierential equation from the given Weyl-Yurko matrix and prove the corresponding uniqueness theorem.

scholarly journals An interior inverse problem for Sturm-Liouville operators with eigenparameter dependent boundary conditions

2011 ◽  
Vol 42 (3) ◽  
pp. 395-403 ◽  
Author(s):  
Wang Yu-Ping
Keyword(s):  
Inverse Problem ◽  
Boundary Conditions ◽  
Interior Point ◽  
Sturm Liouville ◽  
Liouville Operators

In this paper, we consider the inverse problem for Sturm-Liouvilleoperators with eigenparameter dependent boundary conditions and show that thepotential q(x) can be uniquely determined by a set of values of eigenfunctions atsome interior point and parts of two spectra.

Reciprocity gap method for an interior inverse scattering problem

2017 ◽  
Vol 25 (1) ◽  
Author(s):  
Fang Zeng ◽  
Xiaodong Liu ◽  
Jiguang Sun ◽  
Liwei Xu
Keyword(s):  
Inverse Problem ◽  
Uniqueness Theorem ◽  
Inhomogeneous Medium ◽  
Inverse Scattering ◽  
Interior Point ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Cauchy Data ◽  
Point Sources ◽  
Numerical Examples

AbstractWe consider an interior inverse scattering problem of reconstructing the shape of a cavity with inhomogeneous medium inside. We prove a uniqueness theorem for the inverse problem. Using Cauchy data on a curve inside the cavity due to interior point sources, we employ the reciprocity gap method to reconstruct the cavity. Numerical examples are provided to show the effectiveness of the method.

scholarly journals Application of the Finite Element Method to the Nonlinear Inverse Heat Conduction Problem Using Beck’s Second Method

1980 ◽  
Vol 102 (2) ◽  
pp. 168-176 ◽  
Author(s):  
B. R. Bass
Keyword(s):  
Heat Flux ◽  
Inverse Problem ◽  
Finite Element ◽  
Heat Conduction ◽  
Interior Point ◽  
Surface Heat Flux ◽  
Heat Conduction Problem ◽  
Inverse Heat Conduction Problem ◽  
Surface Heat ◽  
Inverse Heat Conduction

The calculation of the surface temperature and surface heat flux from a measured temperature history at an interior point of a body is identified in the literature as the inverse heat conduction problem. This paper presents, to the author’s knowledge, the first application of a solution technique for the inverse problem that utilizes a finite element heat conduction model and Beck’s nonlinear estimation procedure. The technique is applicable to the one-dimensional nonlinear model with temperature-dependent thermophysical properties. The formulation is applied first to a numerical example with a known solution. The example treated is that of a periodic heat flux imposed on the surface of a rod. The computed surface heat flux is compared with the imposed heat flux to evaluate the performance of the technique in solving the inverse problem. Finally, the technique is applied to an experimentally determined temperature transient taken from an interior point of an electrically-heated composite rod. The results are compared with those obtained by applying a finite difference inverse technique to the same data.

AN INVERSE PROBLEM IN THE DYNAMICAL REATOR THEORY

1982 ◽  
Vol 2 (1) ◽  
pp. 9-16 ◽  
Author(s):  
Dexing Feng ◽  
Guangtian Zhu
Keyword(s):  
Inverse Problem
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