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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

IMPACT FACTOR 2018: 0.881
5-year IMPACT FACTOR: 1.170

CiteScore 2018: 0.91

SCImago Journal Rank (SJR) 2018: 0.430
Source Normalized Impact per Paper (SNIP) 2018: 0.969

Mathematical Citation Quotient (MCQ) 2018: 0.66

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Volume 24, Issue 2


Determination of the initial condition in parabolic equations from boundary observations

Dinh Nho Hào / Nguyen Thi Ngoc Oanh
Published Online: 2016-03-24 | DOI: https://doi.org/10.1515/jiip-2015-0055


The problem of determining the initial condition in parabolic equations from boundary observations is studied. It is reformulated as a variational problem and then a formula for the gradient of the functional to be minimized is derived via an adjoint problem. The variational problem is discretized by finite difference splitting methods and solved by the conjugate gradient method. Some numerical examples are presented to show the efficiency of the method. Also as a by-product of the variational method, we propose a numerical scheme for numerically estimating singular values of the solution operator in the inverse problem.

Keywords: Inverse problems; ill-posed problems; initial condition; boundary observations; finite difference splitting method; variational method; singular values

MSC: 65M32; 65N20; 65J20

About the article

Received: 2015-05-29

Revised: 2016-03-12

Accepted: 2016-03-12

Published Online: 2016-03-24

Published in Print: 2016-04-01

Funding Source: Vietnam National Foundation for Science and Technology Development (NAFOSTED)

Award identifier / Grant number: 101.02-2014.54

Citation Information: Journal of Inverse and Ill-posed Problems, Volume 24, Issue 2, Pages 195–220, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/jiip-2015-0055.

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