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

We consider the problem of determining the temperature u(x,t), for (x,t)∈[0,π]×[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 met...

Full description

Saved in:
Bibliographic Details
Published in:Journal of computational and applied mathematics 2013-01, Vol.237 (1), p.432-441
Main Authors: Le, Triet Minh, Pham, Quan Hoang, Dang, Trong Duc, Nguyen, Tuan Huy
Format: Article
Language:English
Subjects:
Backward problem
Coefficients
Computation
Estimates
Ill-posed problem
Mathematical analysis
Mathematical models
Nonhomogeneous
Optimization
Parabolic equation
Regularization
Stability
Time-dependent coefficient
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We consider the problem of determining the temperature u(x,t), for (x,t)∈[0,π]×[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.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2012.06.012