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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

6 Issues per year


IMPACT FACTOR 2016: 0.783
5-year IMPACT FACTOR: 0.792

CiteScore 2016: 0.80

SCImago Journal Rank (SJR) 2016: 0.589
Source Normalized Impact per Paper (SNIP) 2016: 1.125

Mathematical Citation Quotient (MCQ) 2015: 0.43

Online
ISSN
1569-3945
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Volume 23, Issue 5 (Oct 2015)

Issues

Identification of nonlinear heat conduction laws

Herbert Egger
  • AG Numerik und Wissenschaftliches Rechnen, Fachbereich Mathematik, TU Darmstadt, Dolivostr. 15, 64293 Darmstadt, Germany
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/ Jan-Frederik Pietschmann
  • AG Numerik und Wissenschaftliches Rechnen, Fachbereich Mathematik, TU Darmstadt, Dolivostr. 15, 64293 Darmstadt, Germany
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/ Matthias Schlottbom
  • AG Numerik und Wissenschaftliches Rechnen, Fachbereich Mathematik, TU Darmstadt, Dolivostr. 15, 64293 Darmstadt, Germany
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Published Online: 2014-12-11 | DOI: https://doi.org/10.1515/jiip-2014-0030

Abstract

We consider the identification of nonlinear heat conduction laws in stationary and instationary heat transfer problems. Only a single additional measurement of the temperature on a curve on the boundary is required to determine the unknown parameter function on the range of observed temperatures. We first present a new proof of Cannon's uniqueness result for the stationary case, which allows us to derive a corresponding stability estimate, and then extend our argument to instationary problems which are close to steady state.

Keywords: Parameter identification; nonlinear diffusion; quasilinear parabolic problems

MSC: 35R30; 65J22

About the article

Received: 2014-04-09

Revised: 2014-09-26

Accepted: 2014-09-29

Published Online: 2014-12-11

Published in Print: 2015-10-01


Funding Source: DFG

Award identifier / Grant number: IRTG 1529

Funding Source: DFG

Award identifier / Grant number: GSC 233

Funding Source: DFG

Award identifier / Grant number: TRR 154

Funding Source: DFG

Award identifier / Grant number: 1073/1-1

Funding Source: Daimler and Benz Stiftung

Award identifier / Grant number: 32-09/12

Funding Source: ERC

Award identifier / Grant number: EU FP 7 – ERC Consolidator Grant 615216 LifeInverse


Citation Information: Journal of Inverse and Ill-posed Problems, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/jiip-2014-0030.

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