On a Hyperbolic Coefficient Inverse Problem via Partial Dynamic Boundary Measurements
This paper is devoted to the identification of the unknown smooth coefficient c entering the hyperbolic equation c(x)∂t2u−Δu=0 in a bounded smooth domain in ℝd from partial (on part of the boundary) dynamic boundary measurements. In this paper, we prove that the knowledge of the partial Cauchy data...
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| Format: | Article |
| Language: | English |
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Wiley
2010-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2010/561395 |
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| _version_ | 1832549348497424384 |
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| author | Christian Daveau Diane Manuel Douady Abdessatar Khelifi |
| author_facet | Christian Daveau Diane Manuel Douady Abdessatar Khelifi |
| author_sort | Christian Daveau |
| collection | DOAJ |
| description | This paper is devoted to the identification of the unknown smooth coefficient c entering the hyperbolic equation c(x)∂t2u−Δu=0 in a bounded smooth domain in ℝd from partial (on part of the boundary) dynamic boundary measurements. In this paper, we prove that the knowledge of the partial Cauchy data for this class of hyperbolic PDE on any open subset Γ of the boundary determines explicitly the coefficient c provided that c is known outside a bounded domain. Then, through construction of appropriate test functions by a geometrical control method, we derive a formula for calculating the coefficient c from the knowledge of the difference between the local Dirichlet-to-Neumann maps. |
| format | Article |
| id | doaj-art-fc6fce1840fe4d23b0a71bdfce892a7a |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-fc6fce1840fe4d23b0a71bdfce892a7a2025-02-03T06:11:41ZengWileyJournal of Applied Mathematics1110-757X1687-00422010-01-01201010.1155/2010/561395561395On a Hyperbolic Coefficient Inverse Problem via Partial Dynamic Boundary MeasurementsChristian Daveau0Diane Manuel Douady1Abdessatar Khelifi2Département de Mathématiques, CNRS AGM UMR 8088, Université de Cergy-Pontoise, 95302 Cergy-Pontoise Cedex, FranceDépartement de Mathématiques, CNRS AGM UMR 8088, Université de Cergy-Pontoise, 95302 Cergy-Pontoise Cedex, FranceDépartement de Mathématiques, Université des Sciences de Carthage, 7021 Bizerte, TunisiaThis paper is devoted to the identification of the unknown smooth coefficient c entering the hyperbolic equation c(x)∂t2u−Δu=0 in a bounded smooth domain in ℝd from partial (on part of the boundary) dynamic boundary measurements. In this paper, we prove that the knowledge of the partial Cauchy data for this class of hyperbolic PDE on any open subset Γ of the boundary determines explicitly the coefficient c provided that c is known outside a bounded domain. Then, through construction of appropriate test functions by a geometrical control method, we derive a formula for calculating the coefficient c from the knowledge of the difference between the local Dirichlet-to-Neumann maps.http://dx.doi.org/10.1155/2010/561395 |
| spellingShingle | Christian Daveau Diane Manuel Douady Abdessatar Khelifi On a Hyperbolic Coefficient Inverse Problem via Partial Dynamic Boundary Measurements Journal of Applied Mathematics |
| title | On a Hyperbolic Coefficient Inverse Problem via Partial Dynamic Boundary Measurements |
| title_full | On a Hyperbolic Coefficient Inverse Problem via Partial Dynamic Boundary Measurements |
| title_fullStr | On a Hyperbolic Coefficient Inverse Problem via Partial Dynamic Boundary Measurements |
| title_full_unstemmed | On a Hyperbolic Coefficient Inverse Problem via Partial Dynamic Boundary Measurements |
| title_short | On a Hyperbolic Coefficient Inverse Problem via Partial Dynamic Boundary Measurements |
| title_sort | on a hyperbolic coefficient inverse problem via partial dynamic boundary measurements |
| url | http://dx.doi.org/10.1155/2010/561395 |
| work_keys_str_mv | AT christiandaveau onahyperboliccoefficientinverseproblemviapartialdynamicboundarymeasurements AT dianemanueldouady onahyperboliccoefficientinverseproblemviapartialdynamicboundarymeasurements AT abdessatarkhelifi onahyperboliccoefficientinverseproblemviapartialdynamicboundarymeasurements |