1. Wavelets and regularization of the sideways heat equation
- Author
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Qiu, Chun-Yu, Fu, Chu-Li, and Zhu, You-Bin
- Subjects
- *
PERTURBATION theory , *WAVELETS (Mathematics) , *MATHEMATICS , *MATHEMATICAL analysis , *DYNAMICS , *MATHEMATICAL physics , *FUNCTIONAL analysis , *APPROXIMATION theory - Abstract
In this paper, the following inverse heat conduction problem: ut = uxx, x≥0, t≥0, u(x,0) = 0, x≥0 u(1,t) = g(t), t≥0, u&z.sfnc;x→∞ is bounded, is considered again. This problem is severely ill-posed: its solution (if it exists) does not depend continuously on the data; a small perturbation in the data may cause a dramatically large error in the solution for
0 < x < 1 . In this paper, a new wavelet regularization method for this problem is given. Moreover, we can easily find the regularization parameter J such that some sharp stable estimates between the exact solution and the approximate one inHr(R)-norm meaning is given. [Copyright &y& Elsevier]- Published
- 2003
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