A wavelet method for solving backward heat conduction problems. (English) Zbl 1372.65370

Qiu, Chunyu; Feng, Xiaoli

Electron. J. Differ. Equ. 2017, Paper No. 219, 19 p. (2017).

Summary: 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.

MSC:

65T60	Numerical methods for wavelets
65M30	Numerical methods for ill-posed problems for initial value and initial-boundary value problems involving PDEs
35R25	Ill-posed problems for PDEs

Keywords:

backward heat equation; ill-posed problem; regularization; Meyer wavelet; error estimate