Publication Cover
Applicable Analysis
An International Journal
Volume 102, 2023 - Issue 14
120
Views
0
CrossRef citations to date
0
Altmetric
Articles

Determination of a spacewise-dependent heat source by a logarithmic-type regularization method

, &
Pages 3986-4003 | Received 26 Mar 2022, Accepted 12 Jul 2022, Published online: 22 Jul 2022

References

  • Prilepko AI, Tkachenko DS. Inverse problem for a parabolic equation with integral overdetermination. J Inverse Ill-Posed Probl. 2003;11:191–218.
  • Choulli M, Yamamoto M. Conditional stability in determining a heat source. J Inverse Ill-Posed Probl. 2004;12:233–243.
  • Johansson T, Lesnic D. Determination of a spacewise dependent heat source. J Comput Appl Math. 2007;209(1):66–80.
  • Johansson BT, Lesnic D. A variational method for identifying a spacewise-dependent heat source. IMA J Appl Math. 2007;72(6):748–760.
  • Trong DD, Dinh Alain PN, Thanh Nam P. Determine the special term of a two-dimensional heat source. Appl Anal. 2009;88(3):457–474.
  • Yan L, Yang FL, Fu CL. A meshless method for solving an inverse spacewise-dependent heat source problem. J Comput Phys. 2009;228(1):123–136.
  • Hasanov A, Pektaş B. A unified approach to identifying an unknown spacewise dependent source in a variable coefficient parabolic equation from final and integral overdeterminations. Appl Numer Math. 2014;78:49–67.
  • Wang Z, Zhang W, Wu B. Regularized optimization method for determining the space-dependent source in a parabolic equation without iteration. J Comput Anal Appl. 2016;20(6):1107–1126.
  • Qiu S, Zhang W, Peng J. Simultaneous determination of the space-dependent source and the initial distribution in a heat equation by regularizing Fourier coefficients of the given measurements. Adv Math Phys. 2018;2018:1–15.
  • Ahsan M, Hussain I. Haar wavelets multi-resolution collocation analysis of unsteady inverse heat problems. Inverse Probl Sci Eng. 2019;27(11):1498–1520.
  • Hào DN, Huong BV, Oanh NTN, et al. Determination of a term in the right-hand side of parabolic equations. J Comput Appl Math. 2017;309:28–43.
  • Wang Z, Ruan Z, Huang H, et al. Determination of an unknown time-dependent heat source from A nonlocal measurement by finite difference method. Acta Math Appl Sin, English Ser. 2020;36(1):151–165.
  • Hào DN, Quyen TNT, Son NT. Convergence analysis of a Crank–Nicolson Galerkin method for an inverse source problem for parabolic equations with boundary observations. Appl Math Optim. 2021;84(2):2289–2325.
  • Ahsan M, Hussian I. A multi-resolution collocation procedure for time-dependent inverse heat problems. Int J Therm Sci. 2018;128:160–174.
  • Wang JG, Zhou YB, Wei T. Two regularization methods to identify a space-dependent source for the time-fractional diffusion equation. Appl Numer Math. 2013;68:39–57.
  • Ma YK, Prakash P, Deiveegan A. Generalized Tikhonov methods for an inverse source problem of the time-fractional diffusion equation. Chaos Solitons Fractals. 2018;108:39–48.
  • Xiong X, Xue X. A fractional Tikhonov regularization method for identifying a space-dependent source in the time-fractional diffusion equation. Appl Math Comput. 2019;349:292–303.
  • Wang Z, Qiu S, Yu S, et al. Exponential Tikhonov regularization method for solving an inverse source problem of time fractional diffusion equations. J Comput Math. doi:10.4208/jcm.2107-m2020-0133.
  • Ladyzhenskaya OA. The boundary value problems of mathematical physics. New York: Springer-Verlag; 1985.
  • Audeh W, Kittaneh F. Singular value inequalities for compact operators. Linear Algebra Appl. 2012;437(10):2516–2522.
  • Wang Z, Liu J. New model function methods for determining regularization parameters in linear inverse problems. Appl Numer Math. 2009;59(10):2489–2506.
  • Liu JJ, Ni M. A model function method for determining the regularizing parameter in potential approach for the recovery of scattered wave. Appl Numer Math. 2008;58(8):1113–1128.
  • Wang Z, Xu D. On the linear model function method for choosing Tikhonov regularization parameters in linear ill-posed problems. Chin J Eng Math. 2013;30(3):451–466.

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.