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Determine the source term of a two-dimensional heat equation | | Dang Duc Trong
; Truong Trung Tuyen
; Phan Thanh Nam
; Alain Pham Ngoc Dinh
; | | Date: |
11 Jul 2008 | | Abstract: | 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. | | Source: | arXiv, 0807.1812 | | Services: | Forum | Review | PDF | Favorites | |
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