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| Detailed view | Preprint, Working Paper, ... |
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| Available versions: | v1 (2008-07-10) | v2 (2008-07-11) | v3 (2008-07-11) |
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| Determine the spacial term of a two-dimensional heat source |
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| Dang Duc Trong1Alain Pham Ngoc Dinh2Phan Thanh Nam1 |
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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: | UNS-HCMC - University of Natural Sciences HoChiMinh City |
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| 2: | MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans |
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| heat source – ill-posed problem – interpolation method – Fourier series |
| hal-00294612, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00294612 | |
| oai:hal.archives-ouvertes.fr:hal-00294612 | |
| From: Alain Pham Ngoc Dinh | |
| Submitted on: Thursday, 10 July 2008 23:15:15 | |
| Updated on: Friday, 11 July 2008 07:30:08 | |
