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Zbl 1201.65176
Yang, Fan; Fu, Chu-Li
The method of simplified Tikhonov regularization for dealing with the inverse time-dependent heat source problem. (English)
[J] Comput. Math. Appl. 60, No. 5, 1228-1236 (2010). ISSN 0898-1221

Summary: This paper investigates the inverse problem of determining a heat source using a parabolic equation where data are given at some fixed location. The problem is ill-posed, i.e., the solution (if it exists) does not depend continuously on the data. A simplified Tikhonov regularization method is given and an order optimal stability estimate is obtained. A numerical example shows that the regularization method is effective and stable.

MSC 2000:: *65M32 Inverse problems
35K10 Second order parabolic equations, general
80A22 Stefan problems, etc.
80M25 Other numerical methods

Keywords: heat source; simplified Tikhonov method; error estimate

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