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hal-00295103, version 1

## Determine the source term of a two-dimensional heat equation

Dang Duc Trong () 1, Truong Trung Tuyen () 2, Phan Thanh Nam () 1, Alain Pham Ngoc Dinh () 3

Résumé : Let $\Omega$ be a two-dimensional heat conduction body. We consider the problem of determining the heat source $F(x,t)=\varphi(t)f(x,y)$ with $\varphi$ be given inexactly and $f$ be unknown. The problem is nonlinear and ill-posed. By a specific form of Fourier transforms, we shall show that the heat source is determined uniquely by the minimum boundary condition and the temperature distribution in $\Omega$ at the initial time $t=0$ and at the final time $t=1$. Using the methods of Tikhonov's regularization and truncated integration, we construct the regularized solutions. Numerical part is given.

• 1 :  University of Natural Sciences HoChiMinh City (UNS-HCMC)
• University of Natural Sciences- HoChiMinhCity
• 2 :  Department of Mathematics (IU)
• Indiana University
• 3 :  Mathématiques - Analyse, Probabilités, Modélisation - Orléans (MAPMO)
• Université d'Orléans – CNRS : UMR7349
• Domaine : Mathématiques/Equations aux dérivées partielles
• Mots-clés : Error estimate – Fourier transform – ill-posed problem – heat source – Tikhonov's regularization – truncated integration.
• Commentaire : 18 pages

• hal-00295103, version 1
• oai:hal.archives-ouvertes.fr:hal-00295103
• Contributeur :
• Soumis le : Vendredi 11 Juillet 2008, 11:45:02
• Dernière modification le : Vendredi 11 Juillet 2008, 11:57:16