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Solving the backward problem for time-fractional wave equations by the quasi-reversibility regularization method.
- Source :
-
Advances in Computational Mathematics . Dec2023, Vol. 49 Issue 6, p1-26. 26p. - Publication Year :
- 2023
-
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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 10197168
- Volume :
- 49
- Issue :
- 6
- Database :
- Academic Search Index
- Journal :
- Advances in Computational Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 173251446
- Full Text :
- https://doi.org/10.1007/s10444-023-10080-w