Determine the source term of a two-dimensional heat equation
| dc.creator | Trong, Dang Duc | |
| dc.creator | Tuyen, Truong Trung | |
| dc.creator | Nam, Phan Thanh | |
| dc.creator | Dinh, Alain Pham Ngoc | |
| dc.date | 2008-07-11 | |
| dc.date.accessioned | 2026-07-07T09:49:50Z | |
| dc.date.available | 2026-07-07T09:49:50Z | |
| dc.description | Let $Ω$ be a two-dimensional heat conduction body. We consider the problem of determining the heat source $F(x,t)=φ(t)f(x,y)$ with $φ$ 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 $Ω$ 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. | |
| dc.description | 18 pages | |
| dc.identifier | https://arxiv.org/abs/0807.1812 | |
| dc.identifier | http://arxiv.org/abs/0807.1812 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/164733 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35K05, 42B10, 65M32 | |
| dc.title | Determine the source term of a two-dimensional heat equation | |
| dc.type | text |