Identifying Initial Condition in Degenerate Parabolic Equation with Singular Potential
A hybrid algorithm and regularization method are proposed, for the first time, to solve the one-dimensional degenerate inverse heat conduction problem to estimate the initial temperature distribution from point measurements. The evolution of the heat is given by a degenerate parabolic equation with...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2017/1467049 |
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| author | K. Atifi Y. Balouki El-H. Essoufi B. Khouiti |
| author_facet | K. Atifi Y. Balouki El-H. Essoufi B. Khouiti |
| author_sort | K. Atifi |
| collection | DOAJ |
| description | A hybrid algorithm and regularization method are proposed, for the first time, to solve the one-dimensional degenerate inverse heat conduction problem to estimate the initial temperature distribution from point measurements. The evolution of the heat is given by a degenerate parabolic equation with singular potential. This problem can be formulated in a least-squares framework, an iterative procedure which minimizes the difference between the given measurements and the value at sensor locations of a reconstructed field. The mathematical model leads to a nonconvex minimization problem. To solve it, we prove the existence of at least one solution of problem and we propose two approaches: the first is based on a Tikhonov regularization, while the second approach is based on a hybrid genetic algorithm (married genetic with descent method type gradient). Some numerical experiments are given. |
| format | Article |
| id | doaj-art-08032951b8d24ce2abf40e4b8f7c6d21 |
| institution | Kabale University |
| issn | 1687-9643 1687-9651 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-08032951b8d24ce2abf40e4b8f7c6d212025-02-03T01:21:00ZengWileyInternational Journal of Differential Equations1687-96431687-96512017-01-01201710.1155/2017/14670491467049Identifying Initial Condition in Degenerate Parabolic Equation with Singular PotentialK. Atifi0Y. Balouki1El-H. Essoufi2B. Khouiti3Laboratoire de Mathématiques, Informatique et Sciences de l’Ingénieur (MISI), Université Hassan 1er, 26000 Settat, MoroccoLaboratoire de Mathématiques, Informatique et Sciences de l’Ingénieur (MISI), Université Hassan 1er, 26000 Settat, MoroccoLaboratoire de Mathématiques, Informatique et Sciences de l’Ingénieur (MISI), Université Hassan 1er, 26000 Settat, MoroccoLaboratoire de Mathématiques, Informatique et Sciences de l’Ingénieur (MISI), Université Hassan 1er, 26000 Settat, MoroccoA hybrid algorithm and regularization method are proposed, for the first time, to solve the one-dimensional degenerate inverse heat conduction problem to estimate the initial temperature distribution from point measurements. The evolution of the heat is given by a degenerate parabolic equation with singular potential. This problem can be formulated in a least-squares framework, an iterative procedure which minimizes the difference between the given measurements and the value at sensor locations of a reconstructed field. The mathematical model leads to a nonconvex minimization problem. To solve it, we prove the existence of at least one solution of problem and we propose two approaches: the first is based on a Tikhonov regularization, while the second approach is based on a hybrid genetic algorithm (married genetic with descent method type gradient). Some numerical experiments are given.http://dx.doi.org/10.1155/2017/1467049 |
| spellingShingle | K. Atifi Y. Balouki El-H. Essoufi B. Khouiti Identifying Initial Condition in Degenerate Parabolic Equation with Singular Potential International Journal of Differential Equations |
| title | Identifying Initial Condition in Degenerate Parabolic Equation with Singular Potential |
| title_full | Identifying Initial Condition in Degenerate Parabolic Equation with Singular Potential |
| title_fullStr | Identifying Initial Condition in Degenerate Parabolic Equation with Singular Potential |
| title_full_unstemmed | Identifying Initial Condition in Degenerate Parabolic Equation with Singular Potential |
| title_short | Identifying Initial Condition in Degenerate Parabolic Equation with Singular Potential |
| title_sort | identifying initial condition in degenerate parabolic equation with singular potential |
| url | http://dx.doi.org/10.1155/2017/1467049 |
| work_keys_str_mv | AT katifi identifyinginitialconditionindegenerateparabolicequationwithsingularpotential AT ybalouki identifyinginitialconditionindegenerateparabolicequationwithsingularpotential AT elhessoufi identifyinginitialconditionindegenerateparabolicequationwithsingularpotential AT bkhouiti identifyinginitialconditionindegenerateparabolicequationwithsingularpotential |