TV-like regularization for backward parabolic problems
详细信息 查看全文
- 作者：Bin Pan ; Dinghua Xu ; Yinghong Xu and Yue Yu
- 刊名：Mathematical Methods in the Applied Sciences
- 出版年：2017
- 出版时间：15 March 2017
- 年：2017
- 卷：40
- 期：4
- 页码：957-969
- 全文大小：510K
- ISSN：1099-1476
文摘
This paper investigates an inverse problem for parabolic equations backward in time, which is solved by total-variation-like (TV-like, in abbreviation) regularization method with cost function ∥ux∥2. The existence, uniqueness and stability estimate for the regularization problem are deduced in the linear case. For numerical illustration, the variational adjoint method, which presents a simple method to derive the gradient of the optimization functional, is introduced to reconstruct the unknown initial condition for both linear and nonlinear parabolic equations. The conjugate gradient method is used to iteratively search for the optimal approximation. Numerical results validate the feasibility and effectiveness of the proposed algorithm. Copyright