Determine the source term of a two-dimensional heat equation
Duc Trong, Dang ; Trung Tuyen, Truong ; Thanh Nam, Phan ; Pham Ngoc Dinh, Alain
HAL, hal-00295103 / Harvested from HAL
Text on HAL
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.
Publié le : 2008-07-11
Classification:  truncated integration,  Error estimate,  Fourier transform,  ill-posed problem,  heat source,  Tikhonov's regularization,  truncated integration.,  35K05, 42B10, 65M32,  [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] 
@article{hal-00295103,
     author = {Duc Trong, Dang and Trung Tuyen, Truong and Thanh Nam, Phan and Pham Ngoc Dinh, Alain},
     title = {Determine the source term of a two-dimensional heat equation},
     journal = {HAL},
     volume = {2008},
     number = {0},
     year = {2008},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00295103}
}

Duc Trong, Dang; Trung Tuyen, Truong; Thanh Nam, Phan; Pham Ngoc Dinh, Alain. Determine the source term of a two-dimensional heat equation. HAL, Tome 2008 (2008) no. 0, . http://gdmltest.u-ga.fr/item/hal-00295103/