Chunyu Qiu, Xiaoli Feng
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.
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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