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Detailed view Article in peer-reviewed journal
Applicable Analysis 88, 3 (2009) 457-474
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Determine the spacial term of a two-dimensional heat source
Dang Duc Trong1, Alain Pham Ngoc Dinh2, Phan Thanh Nam1

We consider the problem of determining a pair of functions $(u,f)$ satisfying the heat equation $u_t -\Delta u =\varphi(t)f (x,y)$, where $(x,y)\in \Omega=(0,1)\times (0,1)$ and the function $\varphi$ is given. The problem is ill-posed. Under a slight condition on $\varphi$, we show that the solution is determined uniquely from some boundary data and the initial temperature. Using the interpolation method and the truncated Fourier series, we construct a regularized solution of the source term $f$ from non-smooth data. The error estimate and numerical experiments are given.
1:  UNS-HCMC - University of Natural Sciences HoChiMinh City
2:  MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans
heat source – ill-posed problem – interpolation method – Fourier series