On Lavrent’ev-Type Integral Equations in Coefficient Inverse Problems for Wave Equations

Coefficient inverse problems for second- and third-order equations with one or two unknown coefficients are investigated. The initial data are specified as the solution of an equation for a set of sounding sources averaged over time with power-law weights. It is shown that the original nonlinear inv...

Full description

Saved in:
Bibliographic Details
Published in:Computational mathematics and mathematical physics 2021-09, Vol.61 (9), p.1470-1484
Main Authors: Kozlov, A. I., Kokurin, M. Yu
Format: Article
Language:English
Subjects:
Coefficients
Computational Mathematics and Numerical Analysis
Integral equations
Inverse problems
Mathematics
Mathematics and Statistics
Nondestructive testing
Partial Differential Equations
Wave equations
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Coefficient inverse problems for second- and third-order equations with one or two unknown coefficients are investigated. The initial data are specified as the solution of an equation for a set of sounding sources averaged over time with power-law weights. It is shown that the original nonlinear inverse problems can be equivalently reduced to integral equations that are linear or nonlinear depending on the averaging method. It is proved that these equations have a unique solution determining the desired solution of the inverse problems. The results of a numerical experiment concerning the solution of a linear integral equation with a special kernel are presented.
ISSN:0965-5425
1555-6662
DOI:10.1134/S0965542521090128