A regularized optimization method for identifying the space-dependent source and the initial value simultaneously in a parabolic equation

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• 作者：Zewen Wang^a ; ^b ; ^{zwwang@ecit.cn" class="auth_mail} ; ^{zwwang6@gmail.com" class="auth_mail} ; Shufang Qiu^b ; Zhousheng Ruan^a ; ^b ; Wen Zhang^a ; ^b
• 关键词：Inverse problem ; Source inversion ; Inverse initial value ; Parabolic equation ; Regularized optimization
• 刊名：Computers and Mathematics with Applications
• 出版年：April, 2014
• 年：2014
• 卷：67
• 期：7
• 页码：1345-1357
• 全文大小：638 K

文摘

In this paper, a regularized optimization method is proposed for identifying the space-dependent source and the initial value simultaneously in an inverse parabolic equation problem from two over-specified measurements at different instants of time. The solvability of the direct problem is presented and then the inverse problem is formulated into a regularized optimization problem for the stable identification of both the source term and the initial value. Based on a sequence of well-posed direct problems solved by the finite element method, a numerical scheme formulated into a linear system is proposed to implement the regularized optimization problem. Numerical results of three examples show that the proposed method is efficient and robust with respect to data noise.