On a nonlinear inverse problem in viscoelasticity
We consider an inverse problem for determining an inhomogeneity in a viscoelastic body of the Zener type, using Cauchy boundary data, under cyclic loads at low frequency. We show that the inverse problem reduces to the one for the Helmholtz equation and to the same nonlinear Calderon equation given...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Publishing House for Science and Technology
2009-12-01
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| Series: | Vietnam Journal of Mechanics |
| Online Access: | https://vjs.ac.vn/index.php/vjmech/article/view/5649 |
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| _version_ | 1850206944666583040 |
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| author | H. D. Bui S. Chaillat |
| author_facet | H. D. Bui S. Chaillat |
| author_sort | H. D. Bui |
| collection | DOAJ |
| description | We consider an inverse problem for determining an inhomogeneity in a viscoelastic body of the Zener type, using Cauchy boundary data, under cyclic loads at low frequency. We show that the inverse problem reduces to the one for the Helmholtz equation and to the same nonlinear Calderon equation given for the harmonic case. A method of solution is proposed which consists in two steps: solution of a source inverse problem, then solution of a linear Volterra integral equation. |
| format | Article |
| id | doaj-art-b4669ffad5c64c629e17304d86fd2cdf |
| institution | OA Journals |
| issn | 0866-7136 2815-5882 |
| language | English |
| publishDate | 2009-12-01 |
| publisher | Publishing House for Science and Technology |
| record_format | Article |
| series | Vietnam Journal of Mechanics |
| spelling | doaj-art-b4669ffad5c64c629e17304d86fd2cdf2025-08-20T02:10:39ZengPublishing House for Science and TechnologyVietnam Journal of Mechanics0866-71362815-58822009-12-01313-410.15625/0866-7136/31/3-4/5649On a nonlinear inverse problem in viscoelasticityH. D. Bui0S. Chaillat1Ecole Polytechnique/LMS, Palaiseau and Electricite de France/RD/LaMSID, Clamart, FranceGeorgia Institute of Technology/College of Computing, USAWe consider an inverse problem for determining an inhomogeneity in a viscoelastic body of the Zener type, using Cauchy boundary data, under cyclic loads at low frequency. We show that the inverse problem reduces to the one for the Helmholtz equation and to the same nonlinear Calderon equation given for the harmonic case. A method of solution is proposed which consists in two steps: solution of a source inverse problem, then solution of a linear Volterra integral equation.https://vjs.ac.vn/index.php/vjmech/article/view/5649 |
| spellingShingle | H. D. Bui S. Chaillat On a nonlinear inverse problem in viscoelasticity Vietnam Journal of Mechanics |
| title | On a nonlinear inverse problem in viscoelasticity |
| title_full | On a nonlinear inverse problem in viscoelasticity |
| title_fullStr | On a nonlinear inverse problem in viscoelasticity |
| title_full_unstemmed | On a nonlinear inverse problem in viscoelasticity |
| title_short | On a nonlinear inverse problem in viscoelasticity |
| title_sort | on a nonlinear inverse problem in viscoelasticity |
| url | https://vjs.ac.vn/index.php/vjmech/article/view/5649 |
| work_keys_str_mv | AT hdbui onanonlinearinverseprobleminviscoelasticity AT schaillat onanonlinearinverseprobleminviscoelasticity |