Volume 5, Issue 5
Point Sources Identification Problems for Heat Equations

Leevan Ling & Tomoya Takeuchi

DOI:

Commun. Comput. Phys., 5 (2009), pp. 897-913.

Published online: 2009-05

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  • Abstract

We considered the point source identification problems for heat equations from noisy observation data taken at the minimum number of spatially fixed measurement points. We aim to identify the unknown number of sources and their locations along with their strengths. In our previous work, we proved that minimum measurement points needed under the noise-free setting. In this paper, we extend the proof to cover the noisy cases over a border class of source functions. We show that if the regularization parameter is chosen properly, the problem can be transformed into a poles identification problem. A reconstruction scheme is proposed on the basis of the developed theoretical results. Numerical demonstrations in 2D and 3D conclude the paper. 

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@Article{CiCP-5-897, author = {}, title = {Point Sources Identification Problems for Heat Equations}, journal = {Communications in Computational Physics}, year = {2009}, volume = {5}, number = {5}, pages = {897--913}, abstract = {

We considered the point source identification problems for heat equations from noisy observation data taken at the minimum number of spatially fixed measurement points. We aim to identify the unknown number of sources and their locations along with their strengths. In our previous work, we proved that minimum measurement points needed under the noise-free setting. In this paper, we extend the proof to cover the noisy cases over a border class of source functions. We show that if the regularization parameter is chosen properly, the problem can be transformed into a poles identification problem. A reconstruction scheme is proposed on the basis of the developed theoretical results. Numerical demonstrations in 2D and 3D conclude the paper. 

}, issn = {1991-7120}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cicp/7769.html} }
TY - JOUR T1 - Point Sources Identification Problems for Heat Equations JO - Communications in Computational Physics VL - 5 SP - 897 EP - 913 PY - 2009 DA - 2009/05 SN - 5 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cicp/7769.html KW - AB -

We considered the point source identification problems for heat equations from noisy observation data taken at the minimum number of spatially fixed measurement points. We aim to identify the unknown number of sources and their locations along with their strengths. In our previous work, we proved that minimum measurement points needed under the noise-free setting. In this paper, we extend the proof to cover the noisy cases over a border class of source functions. We show that if the regularization parameter is chosen properly, the problem can be transformed into a poles identification problem. A reconstruction scheme is proposed on the basis of the developed theoretical results. Numerical demonstrations in 2D and 3D conclude the paper. 

Leevan Ling & Tomoya Takeuchi. (2020). Point Sources Identification Problems for Heat Equations. Communications in Computational Physics. 5 (5). 897-913. doi:
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