An Inverse Source Problem for Singular Parabolic Equations with Interior Degeneracy
The main purpose of this work is to study an inverse source problem for degenerate/singular parabolic equations with degeneracy and singularity occurring in the interior of the spatial domain. Using Carleman estimates, we prove a Lipschitz stability estimate for the source term provided that additio...
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2018/2067304 |
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| author | Khalid Atifi Idriss Boutaayamou Hamed Ould Sidi Jawad Salhi |
| author_facet | Khalid Atifi Idriss Boutaayamou Hamed Ould Sidi Jawad Salhi |
| author_sort | Khalid Atifi |
| collection | DOAJ |
| description | The main purpose of this work is to study an inverse source problem for degenerate/singular parabolic equations with degeneracy and singularity occurring in the interior of the spatial domain. Using Carleman estimates, we prove a Lipschitz stability estimate for the source term provided that additional measurement data are given on a suitable interior subdomain. For the numerical solution, the reconstruction is formulated as a minimization problem using the output least squares approach with the Tikhonov regularization. The Fréchet differentiability of the Tikhonov functional and the Lipschitz continuity of the Fréchet gradient are proved. These properties allow us to apply gradient methods for numerical solution of the considered inverse source problem. |
| format | Article |
| id | doaj-art-091b40ed2dc941e485427f4f88e7b8b1 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-091b40ed2dc941e485427f4f88e7b8b12025-02-03T05:45:18ZengWileyAbstract and Applied Analysis1085-33751687-04092018-01-01201810.1155/2018/20673042067304An Inverse Source Problem for Singular Parabolic Equations with Interior DegeneracyKhalid Atifi0Idriss Boutaayamou1Hamed Ould Sidi2Jawad Salhi3Faculté des Sciences et Techniques, Université Hassan 1er, Laboratoire MISI, BP 577, Settat 26000, MoroccoFaculté Polydisciplinaire de Ouarzazate, Université Ibn Zohr, BP 638, Ouarzazate 45000, MoroccoFaculté des Sciences et Techniques, Université Hassan 1er, Laboratoire MISI, BP 577, Settat 26000, MoroccoFaculté des Sciences et Techniques, Université Hassan 1er, Laboratoire MISI, BP 577, Settat 26000, MoroccoThe main purpose of this work is to study an inverse source problem for degenerate/singular parabolic equations with degeneracy and singularity occurring in the interior of the spatial domain. Using Carleman estimates, we prove a Lipschitz stability estimate for the source term provided that additional measurement data are given on a suitable interior subdomain. For the numerical solution, the reconstruction is formulated as a minimization problem using the output least squares approach with the Tikhonov regularization. The Fréchet differentiability of the Tikhonov functional and the Lipschitz continuity of the Fréchet gradient are proved. These properties allow us to apply gradient methods for numerical solution of the considered inverse source problem.http://dx.doi.org/10.1155/2018/2067304 |
| spellingShingle | Khalid Atifi Idriss Boutaayamou Hamed Ould Sidi Jawad Salhi An Inverse Source Problem for Singular Parabolic Equations with Interior Degeneracy Abstract and Applied Analysis |
| title | An Inverse Source Problem for Singular Parabolic Equations with Interior Degeneracy |
| title_full | An Inverse Source Problem for Singular Parabolic Equations with Interior Degeneracy |
| title_fullStr | An Inverse Source Problem for Singular Parabolic Equations with Interior Degeneracy |
| title_full_unstemmed | An Inverse Source Problem for Singular Parabolic Equations with Interior Degeneracy |
| title_short | An Inverse Source Problem for Singular Parabolic Equations with Interior Degeneracy |
| title_sort | inverse source problem for singular parabolic equations with interior degeneracy |
| url | http://dx.doi.org/10.1155/2018/2067304 |
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