ON REGULARIZATION OF INVERSE PROBLEM FOR HEAT EQUATION
Journal Title: Современные информационные технологии и ИТ-образование - Year 2017, Vol 13, Issue 1
Abstract
The paper contains new results on spectral methods for solving ill-posed problems using the example of the Cauchy problem for a parabolic equation. A method for regularizing the solution of the inverse problem is proposed. We obtain regularized equation by introducing into the heat equation a biquadratic Laplacian with a coefficient equal to the regularization parameter. This allows us to obtain a regularized solution as a well converging spectral series. It is shown that if the solution of the original problem exists, then the difference between the spectral expansions of the initial and regularized solutions tends to zero when the regularization parameter tends to zero in the space of square summable functions. Using the results of the spectral theory of V.A. Ilyin [4], [5]. Some estimates are obtained for the difference between the exact and regularized solutions.
Authors and Affiliations
Vasily Tikhomirov, Olga Bobyleva
Keywords
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- EP ID EP320799
- DOI 10.25559/SITITO.2017.1.442
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