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On a backward problem for nonlinear time fractional wave equations

Part of: Miscellaneous topics - Partial differential equations Real functions

Published online by Cambridge University Press:  24 November 2021

Jia Wei He  and
Yong Zhou
Jia Wei He
Affiliation:
Faculty of Mathematics and Computational Science, Xiangtan University, Hunan 411105, China (jwhe@gxu.edu.cn)
Yong Zhou
Affiliation:
Faculty of Information Technology, Macau University of Science and Technology, Macau 999078, China (yzhou@xtu.edu.cn) Faculty of Mathematics and Computational Science, Xiangtan University, Hunan 411105, China
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Abstract

In this paper, we concern with a backward problem for a nonlinear time fractional wave equation in a bounded domain. By applying the properties of Mittag-Leffler functions and the method of eigenvalue expansion, we establish some results about the existence and uniqueness of the mild solutions of the proposed problem based on the compact technique. Due to the ill-posedness of backward problem in the sense of Hadamard, a general filter regularization method is utilized to approximate the solution and further we prove the convergence rate for the regularized solutions.

Keywords

fractional wave equationbackward problemexistenceregularization

MSC classification

Primary: 35R11: Fractional partial differential equations
Secondary: 26A33: Fractional derivatives and integrals
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 152 , Issue 6 , December 2022 , pp. 1589 - 1612
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Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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