DETERMINATION OF A TWO-DIMENSIONAL HEAT SOURCE : UNIQUENESS, REGULARIZATION AND ERROR ESTIMATE - CaSciModOT (calcul scientifique et modelisation Orleans-Tours) Accéder directement au contenu
Article Dans Une Revue Journal of Computational and Applied Mathematics Année : 2006

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

Résumé

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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Dates et versions

hal-00009236 , version 1 (29-09-2005)

Identifiants

  • HAL Id : hal-00009236 , version 1

Citer

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, 2006, 191, pp.50-67. ⟨hal-00009236⟩
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