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Université d'Orléans |  |
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Université d'Orléans | |
| HAL : hal-00294612, version 3 |
| arXiv : 0807.1806 |
| Fiche détaillée |  Récupérer au format |
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| Applicable Analysis 88, 3 (2009) 457-474 |
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| Versions disponibles : | v1 (10-07-2008) | v2 (11-07-2008) | v3 (11-07-2008) |
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| Determine the spacial term of a two-dimensional heat source |
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| Dang Duc Trong 1Alain Pham Ngoc Dinh 2 |
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| (2009) |
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| We consider the problem of determining a pair of functions $(u,f)$ satisfying the heat equation $u_t -\Delta u =\varphi(t)f (x,y)$, where $(x,y)\in \Omega=(0,1)\times (0,1)$ and the function $\varphi$ is given. The problem is ill-posed. Under a slight condition on $\varphi$, we show that the solution is determined uniquely from some boundary data and the initial temperature. Using the interpolation method and the truncated Fourier series, we construct a regularized solution of the source term $f$ from non-smooth data. The error estimate and numerical experiments are given. |
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| 1 : | University of Natural Sciences HoChiMinh City (UNS-HCMC) |
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University of Natural Sciences- HoChiMinhCity |
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| 2 : | Mathématiques - Analyse, Probabilités, Modélisation - Orléans (MAPMO) |
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Université d'Orléans – CNRS : UMR7349 |
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| Domaine | : | Mathématiques/Equations aux dérivées partielles |
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| heat source – ill-posed problem – interpolation method – Fourier series |
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| Liste des fichiers attachés à ce document : | ||||||||||
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| hal-00294612, version 3 | |
| http://hal.archives-ouvertes.fr/hal-00294612 | |
| oai:hal.archives-ouvertes.fr:hal-00294612 | |
| Contributeur : Alain Pham Ngoc Dinh | |
| Soumis le : Vendredi 11 Juillet 2008, 11:27:25 | |
| Dernière modification le : Mercredi 11 Novembre 2009, 21:43:14 | |
