Inverse source problem for the hyperbolic equation with a time-dependent principal part

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• 作者：Daijun Jiang^a ; ^{jiangdaijun@mail.ccnu.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Yikan Liu^b ; ^{ykliu@ms.u-tokyo.ac.jp" class="auth_mail" title="E-mail the corresponding author} ; Masahiro Yamamoto^b ; ^{myama@ms.u-tokyo.ac.jp" class="auth_mail" title="E-mail the corresponding author}
• 关键词：35R30 ; 35L20 ; 65M32 ; 65F10 ; 65F22
• 刊名：Journal of Differential Equations
• 出版年：2017
• 出版时间：5 January 2017
• 年：2017
• 卷：262
• 期：1
• 页码：653-681
• 全文大小：1251 K

文摘

In this paper, we investigate the inverse problem on determining the spatial component of the source term in the hyperbolic equation with a time-dependent principal part. Based on a Carleman estimate for general hyperbolic operators, we prove a local stability result of Hölder type in both cases of partial boundary and interior observation data. Numerically, we adopt the classical Tikhonov regularization to reformulate the inverse problem into a related optimization problem, for which we develop an iterative thresholding algorithm by using the corresponding adjoint system. Numerical examples up to three spatial dimensions are presented to demonstrate the accuracy and efficiency of the proposed algorithm.