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...

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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
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description 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.
doi_str_mv 10.1016/j.cam.2012.06.012
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subjects Backward problem
Coefficients
Computation
Estimates
Ill-posed problem
Mathematical analysis
Mathematical models
Nonhomogeneous
Optimization
Parabolic equation
Regularization
Stability
Time-dependent coefficient
title A backward parabolic equation with a time-dependent coefficient: Regularization and error estimates
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