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A spectral method for an axisymmetric backward heat equation

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We consider the inverse time problem for an axisymmetric heat equation. The problem is ill-posed: the solution (if it exists) does not depend continuously on the final data. A spectral method is applied to formulate a regularized solution and some quite sharp error estimates for the regularized solution are given with suitable choices of regularization parameters.
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Keywords: axisymmetric backward heat equation; error estimate; ill-posed problem; spectral method

Document Type: Research Article

Affiliations: 1: College of Science, Henan University of Technology, Zhengzhou 450001, P.R. China 2: School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, P.R. China

Publication date: 2009-12-01

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