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Determining an unknown source in the heat equation by a wavelet dual least squares method

Authors
Journal
Applied Mathematics Letters
0893-9659
Publisher
Elsevier
Publication Date
Volume
22
Issue
5
Identifiers
DOI: 10.1016/j.aml.2008.08.003
Keywords
  • Ill-Posed Problem
  • Determining An Unknown Source
  • Meyer Wavelets
  • Dual Least Squares Method
  • Regularization

Abstract

Abstract We consider the problem of determining an unknown source, which depends only on the spatial variable, in a heat equation. The problem is ill-posed in the sense that the solution (if it exists) does not depend continuously on the data. For a reconstruction of the unknown source from measured data the dual least squares method generated by a family of Meyer wavelet subspaces is applied. An explicit relation between the truncation level of the wavelet expansion and the data error bound is found, under which the convergence result with the error estimate is obtained.

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