A backward parabolic equation with a time-dependent coefficient: Regularization and error estimates

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:237

Article

Triet Minh Le¹  Quan Hoang Pham¹  Trong Duc Dang²  Tuan Huy Nguyen³ 

[1] SaiGon Univ, Dept Math & Applicat, Ho Chi Minh City, Vietnam

[2] Vietnam Natl Univ, Univ Nat Sci, Dept Math, Ho Chi Minh City, Vietnam

[3] Hoa Sen Univ, Dept Sci & Technol, Ho Chi Minh City, Vietnam

关键词: Backward problem;    Ill-posed problem;    Nonhomogeneous;    Parabolic equation;    Time-dependent coefficient;   

DOI  :  10.1016/j.cam.2012.06.012

来源: Elsevier

【 摘 要 】

We consider the problem of determining the temperature u(x, t), for (x, t) is an element of [0, pi] x [0, T) in the parabolic equation with a time-dependent coefficient. This problem is severely ill-posed, i.e., the solution (if it exists) does not depend continuously on the given data. In this paper, we use a modified method for regularizing the problem and derive an optimal stability estimation. A numerical experiment is presented for illustrating the estimate. (c) 2012 Elsevier B.V. All rights reserved.

【 授权许可】

Free