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Mathematical Modelling and Analysis Volume 15, 2010 - Issue 4
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Original Articles

Identification of memory kernels in heat flow measuring heat flux at the ends of the barFootnote*

E. Pais Institute of Mathematics, Tallinn UT, Ehitajate rd 5, Tallinn, 19086, Estonia E-mail: [email protected]
Pages 473-490 | Received 04 Dec 2009, Published online: 10 Feb 2011

References

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  • Janno , J. 2004 . Determination of a time‐ and space‐dependent heat flux relaxation function by means of a restricted Dirichlet‐to‐Neumann operator . Math. Meth. Appl. Sci. , 27 : 1241 – 1260 . doi:10.1002/mma.490.
  • Janno , J. and Wolfersdorf , L. v. 1999 . An inverse problem for identification of a time‐and space‐dependent memory kernel of a special kind in heat conduction . Inverse Problems , 15 : 1455 – 1467 . doi:10.1088/0266–5611/15/6/305.
  • Janno , J. and v , L. 2001 . Wolfersdorf. Identification of a special class of memory kernels in one‐dimensional heat flow . J. Inv. Ill‐Posed Problems , 9 : 389 – 411 .
  • Janno , J. and Wolfersdorf , L. v. 2001 . Identification of memory kernels in one‐dimensional heat flow with boundary conditions of the third kind . Inverse Problems in Engineering , 9 : 179 – 198 . doi:10.1080/174159701088027760.
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  • Nunziato , J. W. 1971 . On heat conduction in materials with memory . Quart. Appl. Math. , 29 : 187 – 204 .
  • Pais , E. 2006 . Degenerate memory kernels identification problem with flux‐type additional conditions . J. Inv. Ill‐Posed Problems , 14 : 397 – 418 . doi:10.1515/156939406777571003.
  • Pais , E. and Janno , J. 2005 . Identification of two degenerate time‐ and space‐dependent kernels in a parabolic equation . Electron. J. Differ. Eqns. , 2005 (108) : 1 – 20 .
  • Pais , E. and Janno , J. 2006 . Inverse problem to determine degenerate memory kernels in heat flux with third kind boundary conditions . Math. Model. Anal. , 11 : 427 – 450 .
  • Pais , E. and Janno , J. 2009 . Recovering Memory Kernels in Heat Flow. Inverse Problems for Non‐Homogeneous Degenerate Memory Kernels , Köln : Lambert Academic Publishing .
  • Petrowski , I.G. 1955 . Vorlesungen über partielle Differentialgleichungen , Leipzig : Teubner . (in German)
  • The financial support of Estonian Science Foundation is gratefully acknowledged (Grant nr. 7728).

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