# DETERMINATION OF A TWO-DIMENSIONAL HEAT SOURCE : UNIQUENESS, REGULARIZATION AND ERROR ESTIMATE

Abstract : Let $Q$ be a heat conduction body and let $\varphi = \varphi(t)$ be given. We consider the problem of finding a two-dimensional heat source having the form $\varphi(t)f(x,y)$ in $Q$. The problem is ill-posed. Assuming $\partial Q$ is insulated and $\varphi \not\equiv 0$, we show that the heat source is defined uniquely by the temperature history on $\partial Q$ and the temperature distribution in $Q$ at the initial time $t = 0$ and at the final time $t = 1$. Using the method of truncated integration and the Fourier transform, we construct regularized solutions and derive explicitly error estimate.
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https://hal.archives-ouvertes.fr/hal-00009236
Contributor : Alain Pham Ngoc Dinh <>
Submitted on : Thursday, September 29, 2005 - 4:09:10 PM
Last modification on : Thursday, May 3, 2018 - 3:32:06 PM
Document(s) archivé(s) le : Thursday, April 1, 2010 - 10:35:02 PM

### Identifiers

• HAL Id : hal-00009236, version 1

### Citation

Dang Duc Trong, Pham Hoang Quan, Alain Pham Ngoc Dinh. DETERMINATION OF A TWO-DIMENSIONAL HEAT SOURCE : UNIQUENESS, REGULARIZATION AND ERROR ESTIMATE. Journal of Computational and Applied Mathematics, Elsevier, 2006, 191, pp.50-67. ⟨hal-00009236⟩

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