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

作者：Wang Zewen^*; Qiu Shufang; Ruan Zhousheng; Zhang Wen

来源：Computers & Mathematics with Applications, 2014, 67(7): 1345-1357.

DOI：10.1016/j.camwa.2014.02.007

• Inverse problem
• Source inversion
• Inverse initial value
• Parabolic equation
• Regularized optimization

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.

• 出版日期2014-4
• 单位东华理工大学