On Lavrent’ev-Type Integral Equations in Coefficient Inverse Problems for Wave Equations
| Autor: | A. I. Kozlov, M. Yu. Kokurin |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Computational Mathematics
Nonlinear system Kernel (image processing) ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION Mathematical analysis MathematicsofComputing_NUMERICALANALYSIS Biharmonic equation Uniqueness Inverse problem Wave equation Hyperbolic partial differential equation Integral equation Mathematics |
| Zdroj: | Computational Mathematics and Mathematical Physics. 61:1470-1484 |
| ISSN: | 1555-6662 0965-5425 |
| DOI: | 10.1134/s0965542521090128 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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