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

Authors:
Triet Minh Le;Quan Hoang Pham;Trong Duc Dang;Tuan Huy Nguyen
Affiliations:
Department of Mathematics and Applications, SaiGon University, 273 An Duong Vuong, Dist. 5, Ho Chi Minh City, Viet Nam;Department of Mathematics and Applications, SaiGon University, 273 An Duong Vuong, Dist. 5, Ho Chi Minh City, Viet Nam;Department of Mathematics, University of Natural Science, Vietnam National University, 227 Nguyen Van Cu, Dist.5, Ho Chi Minh City, Viet Nam;Department of Science and Technology, Hoa Sen University, 8 Nguyen Van Trang, Dist. 1, Ho Chi Minh City, Viet Nam
Venue:
Journal of Computational and Applied Mathematics
Year:
2013

Citing 3
Cited 1

A non-overlap domain decomposition method for the forward-backward heat equation

Journal of Computational and Applied Mathematics - Special issue: Proceedings of the 6th Japan--China joint seminar on numerical mathematics, university of Tsukuba, Japan, 5-9 August 2002
Numerical approximation of solution of nonhomogeneous backward heat conduction problem in bounded region

Mathematics and Computers in Simulation
Splitting-based conjugate gradient method for a multi-dimensional linear inverse heat conduction problem

Journal of Computational and Applied Mathematics

An a posteriori parameter choice rule for the truncation regularization method for solving backward parabolic problems

Journal of Computational and Applied Mathematics

Quantified Score

Hi-index	7.29

Visualization

Abstract

We consider the problem of determining the temperature u(x,t), for (x,t)@?[0,@p]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.