A modified regularization method for a Cauchy problem for heat equation on a two-layer sphere domain

Xiangtuan Xiong, Xiaoxiao Cao, Shumei He and Jin Wen

Applied Mathematics and Computation, 2016, vol. 290, issue C, 240-249

Abstract: In this paper, we study a non-characteristic Cauchy problem for a radially symmetric inverse heat conduction equation in a two-layer domain. This is a severely ill-posed problem in the sense that the solution (if it exists) does not depend continuously on the data. It is well-known that the classical Tikhonov regularization solutions are too smooth and the approximate solutions may lack details that might be contained in the exact solutions. Combining Fourier transform technique with a modified version of the classical Tikhonov regularization, we obtain a regularized solution which is stably convergent to the exact solution with a sharp error estimate.

Keywords: Ill-posed problem; Radially symmetric inverse heat conduction problem; Error estimate; Modified Tikhonov regularization (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:290:y:2016:i:c:p:240-249

DOI: 10.1016/j.amc.2016.06.004

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