Regularization of a backward problem for the inhomogeneous time-fractional wave equation |
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| Authors: | Nguyen Huy Tuan Vo Au Le Nhat Huynh Yong Zhou |
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| Institution: | 1. Institute of Research and Development, Duy Tan University, Da Nang, 550000 Vietnam;2. Applied Analysis Research Group, Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam;3. Faculty of Information Technology, Macau University of Science and Technology, Macau, 999078 China |
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| Abstract: | 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. |
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| Keywords: | backward problem Caputo fractional fractional wave equation regularization |
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