Abstract
This paper is devoted to the backward problem of determining the initial value and initial velocity simultaneously in a time-fractional wave equation, with the aid of extra measurement data at two fixed times. Uniqueness results are obtained by using the analyticity and the asymptotics of the Mittag-Leffler functions provided that the two fixed measurement times are sufficiently close. Since this problem is ill-posed, we propose a quasi-reversibility method whose regularization parameters are given by the a priori parameter choice rule. Finally, several one- and two-dimensional numerical examples are presented to show the accuracy and efficiency of the proposed regularization method.
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Funding
The first author was supported by the NNSF of China (12261082, 11326234), NSF of Gansu Province (145RJZA099), Scientific research project of Higher School in Gansu Province (2014A-012), and Project of NWNU-LKQN2020-08. The second author thanks the National Natural Science Foundation of China (12271277). This work is partly supported by the Open Research Fund of Key Laboratory of Nonlinear Analysis & Applications (Central China Normal University), Ministry of Education, P. R. China.
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Communicated by: Bangti Jin
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Wen, J., Li, ZY. & Wang, YP. Solving the backward problem for time-fractional wave equations by the quasi-reversibility regularization method. Adv Comput Math 49, 80 (2023). https://doi.org/10.1007/s10444-023-10080-w
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DOI: https://doi.org/10.1007/s10444-023-10080-w