A wavelet method for solving backward heat conduction problems

Date

2017-09-14

Authors

Qiu, Chunyu
Feng, Xiaoli

Journal Title

Journal ISSN

Volume Title

Publisher

Texas State University, Department of Mathematics

Abstract

In this article, we consider the backward heat conduction problem (BHCP). This classical problem is more severely ill-posed than some other problems, since the error of the data will be exponentially amplified at high frequency components. The Meyer wavelet method can eliminate the influence of the high frequency components of the noisy data. The known works on this method are limited to the a priori choice of the regularization parameter. In this paper, we consider also a posteriori choice of the regularization parameter. The Holder type stability estimates for both a priori and a posteriori choice rules are established. Moreover several numerical examples are also provided.

Description

Keywords

Backward heat equation, Ill-posed problem; regularization, Meyer wavelet, Error estimate

Citation

Qiu, C., & Feng, X. (2017). A wavelet method for solving backward heat conduction problems. <i>Electronic Journal of Differential Equations, 2017</i>(219), pp. 1-19.

Rights

Attribution 4.0 International

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