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On a backward problem for nonlinear time fractional wave equations

Published online by Cambridge University Press:  24 November 2021

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

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.

Type
Research Article
Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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