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 Detailed view Article in peer-reviewed journal
 Applicable Analysis 88, 3 (2009) 457-474
 Available versions: v1 (2008-07-10) v2 (2008-07-11) v3 (2008-07-11)
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 Determine the spacial term of a two-dimensional heat source
 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.
 Keyword(s) : heat source – ill-posed problem – interpolation method – Fourier series
 hal-00294612, version 3 http://hal.archives-ouvertes.fr/hal-00294612 oai:hal.archives-ouvertes.fr:hal-00294612 From: Alain Pham Ngoc Dinh <> Submitted on: Friday, 11 July 2008 11:27:25 Updated on: Wednesday, 11 November 2009 21:43:14