436
Views
0
CrossRef citations to date
0
Altmetric
Articles

Source strength identification problem for the three-dimensional inverse heat conduction equations

, &
Pages 827-838 | Received 03 Feb 2018, Accepted 24 Aug 2019, Published online: 16 Sep 2019

References

  • Ling L, Takeuchi T. Point sources identification problems for heat equations. Commun Comput Phys. 2009;5:897–913.
  • Liang Y, Fu CL, Yang FL. The method of fundamental solutions for the inverse heat source problem. Eng Anal Bound Elem. 2008;32:216–222. doi: 10.1016/j.enganabound.2007.08.002
  • Hon YC, Li M, Melnikov YA. Inverse source identification by Green’s function. Eng Anal Bound Elem. 2010;34:352–358. doi: 10.1016/j.enganabound.2009.09.009
  • Duda P. Solution of inverse heat conduction problem using the Tikhonov regularization method. J Therm Sci. 2017;26:60–65. doi: 10.1007/s11630-017-0910-2
  • Yi Z, Murio DA. Source term identification in 1-D IHCP. Comput Math Appl. 2004;47:1921–1933. doi: 10.1016/j.camwa.2002.11.025
  • Qian A, Li Y. Optimal error bound and generalized Tikhonov regularization for identifying an unknown source in the heat equation. J Math Chem. 2011;49:765–775. doi: 10.1007/s10910-010-9774-3
  • Liang Y, Yang FL, Fu CL. A new numerical method for the inverse source problem from a Bayesian perspective. Int J Numer Meth Eng. 2015;85(11):1460–1474.
  • Cheng W, Zhao LL, Fu CL. Source term identification for an axisymmetric inverse heat conduction problem. Comput Math Appl. 2010;59(1):142–148. doi: 10.1016/j.camwa.2009.08.038
  • Cannon JR, Perezesteva S. Uniqueness and stability of 3D heat sources. Inverse Probl. 1999;7:57–62. doi: 10.1088/0266-5611/7/1/006
  • Choulli M, Yamamoto M. Conditional stability in determining a heat source. J Inverse Illposed Probl. 2004;12:233–243. doi: 10.1515/1569394042215856
  • Shidfar A, Zakeri A, Neisi A. A two-dimensional inverse heat conduction problem for estimating heat source. Int J Math Math Sci. 2005;10:1633–1641. doi: 10.1155/IJMMS.2005.1633
  • Huang CH, Ozisik MN. Inverse problem of determining the unknown strength of an internal plane heat source. J Franklin Inst. 1992;329:751–764. doi: 10.1016/0016-0032(92)90086-V
  • Huang CH, Li JX, Kim S. An inverse problem in estimating the strength of contaminant source for groundwater systems. Appl Math Model. 2008;32:417–431. doi: 10.1016/j.apm.2006.12.009
  • Gaikwad KR, Ghadle KP. Three dimensional non-homogeneous thermoelastic problem in a thick rectangular plate due to internal heat generation. South Afr J Pure Appl Math. 2011;5:26–38.
  • Ozisik MN. Heat conduction. 2nd ed. New York: Wiley-Interscience; 1993.
  • Min T, Geng B, Ren J. Inverse estimation of the initial condition for the heat equation. Int J Pure Appl Math. 2013;82:581–593. doi: 10.12732/ijpam.v82i4.7

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.