Inverse problem for diffusion operators on the finite interval

2014 ◽  
Author(s):  
Murat Sat ◽  
Etibar S. Panakhov
Keyword(s):  
Inverse Problem ◽  
Finite Interval

scholarly journals An inverse problem for the non-self-adjoint matrix Sturm-Liouville operator

2018 ◽  
Vol 50 (1) ◽  
pp. 71-102 ◽  
Author(s):  
Natalia Pavlovna Bondarenko
Keyword(s):  
Inverse Problem ◽  
Liouville Operator ◽  
Finite Interval ◽  
Spectral Characteristics ◽  
Sufficient Conditions ◽  
Adjoint Matrix ◽  
Method Of Spectral Mappings ◽  
Sturm Liouville ◽  
Necessary And Sufficient

The inverse problem of spectral analysis for the non-self-adjoint matrix Sturm-Liouville operator on a finite interval is investigated. We study properties of the spectral characteristics for the considered operator, and provide necessary and sufficient conditions for the solvability of the inverse problem. Our approach is based on the constructive solution of the inverse problem by the method of spectral mappings. The characterization of the spectral data in the self-adjoint case is given as a corollary of the main result.

scholarly journals Recovery of the matrix quadratic differential pencil from the spectral data

2016 ◽  
Vol 24 (3) ◽  
Author(s):  
Natalia Bondarenko
Keyword(s):  
Banach Space ◽  
Inverse Problem ◽  
Spectral Data ◽  
Quadratic Differential ◽  
Finite Interval ◽  
Spectral Characteristics ◽  
The Matrix ◽  
Method Of Spectral Mappings ◽  
Sturm Liouville ◽  
Liouville Operators

AbstractWe consider a pencil of matrix Sturm–Liouville operators on a finite interval. We study the properties of its spectral characteristics and inverse problems that consist in the recovering of the pencil by the spectral data, that is, eigenvalues and so-called weight matrices. This inverse problem is reduced to a linear equation in a Banach space by the method of spectral mappings. A constructive algorithm for the solution of the inverse problem is provided.

scholarly journals An inverse spectral problem for non-selfadjoint Sturm-Liouville operators with nonseparated boundary conditions

2012 ◽  
Vol 43 (2) ◽  
pp. 289-299 ◽  
Author(s):  
Vjacheslav Yurko
Keyword(s):  
Inverse Problem ◽  
Boundary Conditions ◽  
Spectral Problem ◽  
Uniqueness Theorem ◽  
Inverse Spectral Problem ◽  
Finite Interval ◽  
Spectral Characteristics ◽  
Nonseparated Boundary Conditions ◽  
Sturm Liouville ◽  
Liouville Operators

Non-selfadjoint Sturm-Liouville operators on a finite interval with nonseparated boundary conditions are studied. We establish properties of the spectral characteristics and investigate an inverse problem of recovering the operators from their spectral data. For this inverse problem we prove a uniqueness theorem and provide a procedure for constructing the solution.

scholarly journals Spectral analysis for differential operators with singularities

2004 ◽  
Vol 2004 (2) ◽  
pp. 165-182 ◽  
Author(s):  
Vjacheslav Anatoljevich Yurko
Keyword(s):  
Inverse Problem ◽  
Spectral Analysis ◽  
Singular Point ◽  
Boundary Value Problem ◽  
Differential Operators ◽  
Finite Interval ◽  
Boundary Value ◽  
Spectral Characteristics ◽  
Second Order Differential Equations ◽  
Associated Functions

Nonselfadjoint boundary value problems for second-order differential equations on a finite interval with nonintegrable singularities inside the interval are considered under additional sewing conditions for solutions at the singular point. We study properties of the spectrum, prove the completeness of eigen- and associated functions, and investigate the inverse problem of recovering the boundary value problem from its spectral characteristics.

scholarly journals A unuqueness theorem for Sturm-Lioville operators with eigenparameter dependent boundary conditions

2012 ◽  
Vol 43 (1) ◽  
pp. 145-152 ◽  
Author(s):  
Yu-Ping Wang
Keyword(s):  
Boundary Condition ◽  
Inverse Problem ◽  
Boundary Conditions ◽  
Uniqueness Theorem ◽  
Linear Function ◽  
Spectral Parameter ◽  
Finite Interval ◽  
Sturm Liouville ◽  
Fractional Linear Function ◽  
Liouville Operators

In this paper, we discuss the inverse problem for Sturm- Liouville operators with boundary conditions having fractional linear function of spectral parameter on the finite interval $[0, 1].$ Using Weyl m-function techniques, we establish a uniqueness theorem. i.e., If q(x) is prescribed on $[0,\frac{1}{2}+\alpha]$ for some $\alpha\in [0,1),$ then the potential $q(x)$ on the interval $[0, 1]$ and fractional linear function $\frac{a_2\lambda+b_2}{c_2\lambda+d_2}$  of the boundary condition are uniquely determined by a subset $S\subset \sigma (L)$ and fractional linear function $\frac{a_1\lambda+b_1}{c_1\lambda+d_1}$ of the boundary condition.

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