Determination of a term in the right-hand side of parabolic equations

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• 作者：Dinh Nho Hà ; o^a ; ^{hao@math.ac.vn" class="auth_mail" title="E-mail the corresponding author} ; Bui Viet Huong^b ; ^{buiviethuong84@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; Nguyen Thi Ngoc Oanh^b ; ^{oanhntn.tn@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; Phan Xuan Thanh^c ; ^{thanh.phanxuan@hust.vn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Inverse source problems ; Integral observations ; Least squares method ; Tikhonov regularization ; Finite element method ; Conjugate gradient method
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2017
• 出版时间：1 January 2017
• 年：2017
• 卷：309
• 期：Complete
• 页码：28-43
• 全文大小：1821 K

文摘

The inverse problem of determining a term in the right hand side of parabolic equations from integral observations is investigated. The observations can be regarded as generalized interior point observations which are collected in practice. The problem is then reformulated as a least squares problem in coupling with a Tikhonov regularization term. It is proved that the Tikhonov functional is Fréchet differentiable and a formula for the gradient is derived via an adjoint problem. The variational problem is discretized by the finite element method, the convergence of which is proved. The discretized variational problem is numerically solved by the conjugate gradient method. Some numerical examples are presented for showing the efficiency of the method.