A half‐inverse problem for singular diffusion operator with certain boundary conditions

2020 ◽  
Author(s):  
Abdullah Ergün ◽  
Rauf Amirov
Keyword(s):  
Inverse Problem ◽  
Boundary Conditions ◽  
Diffusion Operator ◽  
Singular Diffusion ◽  
Half Inverse Problem

scholarly journals Half inverse problem for the impulsive diffusion operator with discontinuous coefficient

Filomat ◽  
2016 ◽  
Vol 30 (1) ◽  
pp. 157-168 ◽  
Author(s):  
Yaşar Çakmak ◽  
Seval Işık
Keyword(s):  
Inverse Problem ◽  
Discontinuous Coefficient ◽  
Diffusion Operator ◽  
Impulsive Diffusion ◽  
Half Inverse Problem

The half inverse problem is to construct coefficients of the operator in a whole interval by using one spectrum and potential known in a semi interval. In this paper, by using the Hocstadt-Lieberman and Yang-Zettl?s methods we show that if p(x) and q(x) are known on the interval (?/2,?), then only one spectrum suffices to determine p (x),q(x) functions and ?,h coefficients on the interval (0,?) for impulsive diffusion operator with discontinuous coefficient.

Reconstruction of the Diffusion Operator from Nodal Data

2010 ◽  
Vol 65 (1-2) ◽  
pp. 100-106 ◽  
Author(s):  
Chuan-Fu Yang
Keyword(s):  
Inverse Problem ◽  
Diffusion Equation ◽  
Boundary Conditions ◽  
Finite Interval ◽  
Dense Subset ◽  
Diffusion Operator ◽  
Nodal Points ◽  
Nodal Data

AbstractIn this paper, we deal with the inverse problem of reconstructing the diffusion equation on a finite interval. We prove that a dense subset of nodal points uniquely determine the boundary conditions and the coefficients of the diffusion equation. We also provide constructive procedure for them.

scholarly journals On half inverse problem for differential pencils with the spectral parameter in boundary conditions

2011 ◽  
Vol 42 (3) ◽  
pp. 355-364 ◽  
Author(s):  
Sergey Buterin
Keyword(s):  
Inverse Problem ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Spectral Parameter ◽  
Finite Interval ◽  
A Priori ◽  
Half Inverse Problem ◽  
Differential Pencils ◽  
Parameter Dependent ◽  
The Uniqueness Theorem

A second-order differential pencil on a finite interval with spectral parameter dependent boundary conditions is considered. The inverse problem is studied of recovering the coefficients of the boundary value problem from its spectrum, provided that on one half of the interval they are known a priori. The uniqueness theorem for this inverse problem is proved and a constructive procedure for finding its solution is obtained.

The inverse problem of recovering the coefficients of a differential equations on a graph

2020 ◽  
Vol 28 (5) ◽  
pp. 727-738
Author(s):  
Victor Sadovnichii ◽  
Yaudat Talgatovich Sultanaev ◽  
Azamat Akhtyamov
Keyword(s):  
Inverse Problem ◽  
Inverse Problems ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Finite Number ◽  
Characteristic Equation ◽  
Arbitrary Number ◽  
New Class ◽  
Finite Set

AbstractWe consider a new class of inverse problems on the recovery of the coefficients of differential equations from a finite set of eigenvalues of a boundary value problem with unseparated boundary conditions. A finite number of eigenvalues is possible only for problems in which the roots of the characteristic equation are multiple. The article describes solutions to such a problem for equations of the second, third, and fourth orders on a graph with three, four, and five edges. The inverse problem with an arbitrary number of edges is solved similarly.

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.

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