Skip Navigation



IMA Journal of Applied Mathematics Advance Access published online on August 20, 2009
IMA Journal of Applied Mathematics, doi:10.1093/imamat/hxp026
This Article
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Hào, D. N.
Right arrow Articles by Lesnic, D.
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© The Author 2009. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Regularization of parabolic equations backward in time by a non-local boundary value problem method

Dinh Nho Hào{dagger}

Hanoi Institute of Mathematics, 18 Hoang Quoc Viet Road, 10307 Hanoi, Vietnam

Nguyen Van Duc{ddagger}

Department of Mathematics, Vinh University, Vinh City, Vietnam

D. Lesnic§

Department of Applied Mathematics, University of Leeds, Leeds LS2 9JT, UK

{dagger} Corresponding author. Email: hao{at}math.ac.vn

{ddagger} Email: nguyenvanducdhv{at}gmail.com

§ Email: amt5ld{at}maths.leeds.ac.uk

Received on January 21, 2009; Accepted on July 22, 2009

Let H be a Hilbert space with norm ||·||, A: D(A) sub H -> H a positive definite, self-adjoint operator with compact inverse on H, and T and {epsilon} are given positive numbers. The ill-posed parabolic equation backward in time


Formula

is regularized by the well-posed non-local boundary value problem


Formula

with a > 1 being given and {alpha} > 0, the regularization parameter. A priori and a posteriori parameter choice rules are suggested which yield order optimal regularization methods. Numerical results based on the boundary element method are presented and discussed to confirm the theory.

Keywords: parabolic equations backward in time; ill-posed problems; regularization; non-local boundary value problems; a priori and a posteriori parameter choice rules.


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer: Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.