Regularization of a backward problem for the inhomogeneous time‐fractional wave equation

In this paper, we consider a backward problem for an inhomogeneous time‐fractional wave equation in a general bounded domain. Such a backward problem is of practically great importance because we often do not know the initial density of substance, but we can observe the density at a positive moment....

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Bibliographic Details
Published in:Mathematical methods in the applied sciences 2020-05, Vol.43 (8), p.5450-5463
Main Authors: Huy Tuan, Nguyen, Au, Vo, Nhat Huynh, Le, Zhou, Yong
Format: Article
Language:English
Subjects:
backward problem
Caputo fractional
Density
fractional wave equation
Regularization
Regularization methods
Wave equations
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Summary:In this paper, we consider a backward problem for an inhomogeneous time‐fractional wave equation in a general bounded domain. Such a backward problem is of practically great importance because we often do not know the initial density of substance, but we can observe the density at a positive moment. The existence and regularity for the backward problem are investigated. The backward problem is ill‐posed, and we propose a regularizing scheme by using a modified regularization method. We also prove the convergence rate for the regularized solution by using some a priori regularization parameter choice rule.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.6285