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Volume 34, Issue 3
The Method of Fundamental Solution for a Radially Symmetric Heat Conduction Problem with Variable Coefficient

Rui Ma, Xiangtuan Xiong & Mohammed Elmustafa Amin

DOI: 10.4208/jpde.v34.n3.4

J. Part. Diff. Eq., 34 (2021), pp. 258-267.

Published online: 2021-07

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  • Abstract

We consider an inverse heat conduction problem with variable coefficient on an annulus domain. In many practice applications, we cannot know the initial temperature during heat process, therefore we consider a non-characteristic Cauchy problem for the heat equation. The method of fundamental solutions is applied to solve this problem. Due to ill-posedness of this problem, we first discretize the problem and then regularize it in the form of discrete equation. Numerical tests are conducted for showing the effectiveness of the proposed method.

  • Keywords

Inverse heat conduction problem, method of fundamental solutions (MFS), Cauchy problem, Ill-posed problem.

  • AMS Subject Headings

35K05, 65M32, 35R30

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

xiongxt@gmail.com (Xiangtuan Xiong)

  • BibTex
  • RIS
  • TXT
@Article{JPDE-34-258, author = {Ma , RuiXiong , Xiangtuan and Amin , Mohammed Elmustafa}, title = {The Method of Fundamental Solution for a Radially Symmetric Heat Conduction Problem with Variable Coefficient}, journal = {Journal of Partial Differential Equations}, year = {2021}, volume = {34}, number = {3}, pages = {258--267}, abstract = {

We consider an inverse heat conduction problem with variable coefficient on an annulus domain. In many practice applications, we cannot know the initial temperature during heat process, therefore we consider a non-characteristic Cauchy problem for the heat equation. The method of fundamental solutions is applied to solve this problem. Due to ill-posedness of this problem, we first discretize the problem and then regularize it in the form of discrete equation. Numerical tests are conducted for showing the effectiveness of the proposed method.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v34.n3.4}, url = {http://global-sci.org/intro/article_detail/jpde/19323.html} }
TY - JOUR T1 - The Method of Fundamental Solution for a Radially Symmetric Heat Conduction Problem with Variable Coefficient AU - Ma , Rui AU - Xiong , Xiangtuan AU - Amin , Mohammed Elmustafa JO - Journal of Partial Differential Equations VL - 3 SP - 258 EP - 267 PY - 2021 DA - 2021/07 SN - 34 DO - http://doi.org/10.4208/jpde.v34.n3.4 UR - https://global-sci.org/intro/article_detail/jpde/19323.html KW - Inverse heat conduction problem, method of fundamental solutions (MFS), Cauchy problem, Ill-posed problem. AB -

We consider an inverse heat conduction problem with variable coefficient on an annulus domain. In many practice applications, we cannot know the initial temperature during heat process, therefore we consider a non-characteristic Cauchy problem for the heat equation. The method of fundamental solutions is applied to solve this problem. Due to ill-posedness of this problem, we first discretize the problem and then regularize it in the form of discrete equation. Numerical tests are conducted for showing the effectiveness of the proposed method.

Rui Ma, Xiangtuan Xiong & Mohammed Elmustafa Amin. (2021). The Method of Fundamental Solution for a Radially Symmetric Heat Conduction Problem with Variable Coefficient. Journal of Partial Differential Equations. 34 (3). 258-267. doi:10.4208/jpde.v34.n3.4
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