96
Views
4
CrossRef citations to date
0
Altmetric
Articles

Reconstruction of a Source Term in a Parabolic Integro-Differential Equation from Final Data

&
Pages 199-219 | Received 30 Nov 2010, Accepted 31 Mar 2011, Published online: 24 Jun 2011

References

  • Ayapbergenova A.T. Kabanikhin S.I. and Lorenzi A. Justification of optimization methods for inverse integro-differential hyperbolic problems . J. Inverse Ill-Posed Probl ., 12 5 457 – 479 , 2004 . doi: 10.1515/1569394042531341 .
  • Hasanov A. . Simultaneous determination of source terms in a linear parabolic problem from the final overdetermination: Weak solution approach . J. Math. Anal. Appl ., 330 2 766 – 779 , 2007 . doi: 10.1016/j.jmaa.2006.08.018 .
  • Isakov V. Inverse parabolic problems with the final overdetermination . Comm. Pure Appl. Math ., 44 2 185 – 209 , 1991 . doi: 10.1002/cpa.3160440203 .
  • Janno J. 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 11 1241 – 1260 , 2004 . doi: 10.1002/mma.490 .
  • Janno J. and Kasemets K. A positivity principle for parabolic integro-differential equations and inverse problems with final overdetermination . Inverse Probl. Imaging , 3 1 17 – 41 , 2009 . doi: 10.3934/ipi.2009.3.17 .
  • Janno J. and Lorenzi A. Recovering memory kernels in parabolic transmission problems . J. Inverse Ill-Posed Probl ., 16 3 239 – 266 , 2008 . doi: 10.1515/JIIP.2008.015 .
  • Janno J. and Wolfersdorf L.v. . Inverse problems for memory kernels by laplace transform methods . Z. Anal. Anwend ., 19 2 489 – 510 , 2000 .
  • Janno J. and Wolfersdorf L.v. . Identification of memory kernels in one-dimensional heat flow with boundary conditions of the third kind . Inverse Probl. Eng ., 9 2 179 – 198 , 2001 . doi: 10.1080/174159701088027760 .
  • Kabanikhin , S.I. and Lorenzi , A. 1999 . Identification Problems of Wave Phenomena. Theory and Numerics , Utrecht : VSP .
  • Ladyzhenskaya O.A. , olonnikov V.A. S. and Ural'tseva N.N. Linear and Quasilinear Equations of Parabolic Type . American Mathematical Society , Providence, RI , 1968 .
  • Lorenzi A. An identification problem for a conserved phase-field model with memory . Math. Meth. Appl. Sci ., 28 11 1315 – 1339 , 2005 . doi: 10.1002/mma.614 .
  • Lorenzi A. and Mola G. Identification of unknown terms in convolution integrodifferential equations in a Banach space . J. Inverse Ill-Posed Probl ., 18 3 321 – 355 , 2010 . doi: 10.1515/JIIP.2010.013 .
  • Pais E. Identification of memory kernels in heat flow measuring heat flux at the ends of the bar . Math. Model. Anal ., 15 4 473 – 490 , 2010 . doi: 10.3846/1392-6292.2010.15.473-490 .
  • Pais E. and Janno J. Inverse problem to determine degenerate memory kernels in heat flux with third kind boundary conditions . Math. Model. Anal ., 11 4 427 – 450 , 2006 . doi: 10.1080/13926292.2006.9637329 .
  • Solonnikov V.A. On Boundary Value Problems for General Parabolic Systems of Differential Equations . Proc. Steklov Inst. Math., 83, Moscow, 1968. (in Russian)
  • Zeidler , E. 1995 . Applied Functional Analysis. Main Principles and Their Applications , New York : Springer .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.