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.
MSC:
| 65M32 | Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs |
| 35K10 | Second-order parabolic equations |
| 80A22 | Stefan problems, phase changes, etc. |
| 80M25 | Other numerical methods (thermodynamics) (MSC2010) |
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