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The method of simplified Tikhonov regularization for dealing with the inverse time-dependent heat source problem. (English) Zbl 1201.65176
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.

65M32Inverse problems (IVP of PDE, numerical methods)
35K10Second order parabolic equations, general
80A22Stefan problems, phase changes, etc.
80M25Other numerical methods (thermodynamics)
Full Text: DOI
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