Regularization of ill-posed problem for evolution equation with nonlocal operator

Authors

Nguyen Minh Hai Department of Mathematics Economics, Faculty of Data Science in Business, Ho Chi Minh University of Banking, Ho Chi Minh City, Vietnam https://orcid.org/0000-0002-1825-0097
Nguyen Hoang Luc Department of Mathematics Economics, Faculty of Data Science in Business, Ho Chi Minh University of Banking, Ho Chi Minh City, Vietnam https://orcid.org/0000-0002-1825-0097
Ho Duy Binh Faculty of Fundamential Science, Nguyen Hue University - Second Army Academy, Vietnam https://orcid.org/0009-0004-2017-673X
Hoang Tuan Nguyen Department of Applied Mathematics, Faculty of Applied Science, Ho Chi Minh City University of Technology (HCMUT), 268, Ly Thuong Kiet, District 10, Ward 14, Ho Chi Minh City, Vietnam Corresponding Author https://orcid.org/0000-0002-1825-0097

DOI:

https://doi.org/10.61383/ejam.20242382

Keywords:

Fractional elliptic equation, Mittag-Leffler functions, initial inverse problem, ill-posed problem

Abstract

The paper deals with the ill-posedness of the backward problem for fractional evolution equation. The main contribution of our paper is to construct the regularized solution using the Fourier truncation method. We also derive estimates between the regularized solution and the sought solution. Error estimates are obtained in $L^2$ and Hilbert space scales $\mathbb H^\mu$. Our main analysis is based on the estimation of the Mittag-Leffler functions. To the best of the author's knowledge, there are not any results for focusing the regularization of backward problem for elliptic equations with nonlocal operator.

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Published

2024 Sep 05

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Vol. 2 No. 3 (2024): Early Pub Issue

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Research Article

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[1]

“Regularization of ill-posed problem for evolution equation with nonlocal operator”, Electron. J. Appl. Math., vol. 2, no. 3, pp. 27–41, Sep. 2024, doi: 10.61383/ejam.20242382.

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