Electron. J. Differential Equations, Vol. 2017 (2017), No. 219, pp. 1-19.

A wavelet method for solving backward heat conduction problems

Chunyu Qiu, Xiaoli Feng

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.

Submitted March 29, 2017. Published September 14, 2017.
Math Subject Classifications: 65T60, 65M30, 35R25.
Key Words: Backward heat equation; Ill-posed problem; regularization; Meyer wavelet; error estimate.

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Chunyu Qiu
School of Mathematics and Statistics
Lanzhou University
Lanzhou 730000, China
email: qcy@lzu.edu.cn
Xiaoli Feng
School of Mathematics and Statistics
Xidian University
Xi'an 710071, China
email: xiaolifeng@xidian.edu.cn

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