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Simplified Tikhonov and Fourier regularization methods on a general sideways parabolic equation. (English) Zbl 1055.65106

The inverse problem for sideways parabolic equation in the quarter of the spatial-time plane is considered. This type problem arises in different fields of practice when it is necessary to determine the surface temperature from a measured temperature history at a fixed location inside of the body. The studied problem is a severally ill-posed one: a small perturbation in the data may cause sufficiently large errors in the solution of the problem. For this reason the author suggests the regularization procedures by Tikhonov’s method and the method of Fourier transformation for the solution of the considered inverse problem. Results of numerical calculations are given in the end of the work.

MSC:

65M32 Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs
35K05 Heat equation
35R30 Inverse problems for PDEs
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
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