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A modified Tikhonov regularization method for an axisymmetric backward heat equation
Authors:Wei Cheng  Chu Li Fu
Affiliation:1. College of Science, He’nan University of Technology, Zhengzhou, 450001, P. R. China
2. School of Mathematics and Statistics, Lanzhou University, Lanzhou, 730000, P. R. China
Abstract:
This paper deals with the inverse time problem for an axisymmetric heat equation. The problem is ill-posed. A modified Tikhonov regularization method is applied to formulate regularized solution which is stably convergent to the exact one. Meanwhile, a logarithmic-Hölder type error estimate between the approximate solution and exact solution is obtained by introducing a rather technical inequality and improving a priori smoothness assumption.
Keywords:Ill-posed problem   axisymmetric backward heat equation   regularization   error estimate
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