Abstract
We consider the spectral truncation as the regularization for an ill-posed non-homogeneous parabolic final value problem, and obtain error estimates under a general source condition when the data, which consist of the non-homogeneous term as well as the final value, are noisy. The resulting error estimate is compared with the corresponding estimate under the Lavrentieve method, and showed that the truncation method has no index of saturation.
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Acknowledgements
The first version of this work was completed while the author was a visiting mathematician at Sun Yat-sen University, Guanzhou, China, during the period June 13 to July 8, 2019. The support and the warm hospitality received from Prof. Hongqi Yang are gratefully acknowledged.
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Communicating Editor: A K Nandakumaran
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Nair, M.T. On truncated spectral regularization for an ill-posed evolution equation. Proc Math Sci 131, 30 (2021). https://doi.org/10.1007/s12044-021-00632-9
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DOI: https://doi.org/10.1007/s12044-021-00632-9