Nonhomogeneous heat equation: Identification and regularization for the inhomogeneous term |
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| Authors: | Dang Duc Trong |
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| Institution: | a Mathematics Department, Viet Nam National University, 227 Nguyen Van Cu, HoChiMinh City, District 5, Viet Nam
b Mathematics Department, Mapmo UMR 6628, BP 67-59, 45067 Orleans cedex, France |
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| Abstract: | We study the nonhomogeneous heat equation under the form ut−uxx=φ(t)f(x), where the unknown is the pair of functions (u,f). Under various assumptions about the function φ and the final value in t=1, i.e., g(x), we propose different regularizations on this ill-posed problem based on the Fourier transform associated with a Lebesgue measure. For φ?0 the solution is unique. |
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| Keywords: | Identification Regularization Error estimations |
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