## 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)

### Keywords:

heat source; simplified Tikhonov method; error estimate
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### References:

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