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


Point Sources Identification Problems for Heat Equations

Leevan Ling 1*, Tomoya Takeuchi 2

1 Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong.
2 Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, Meguro, Tokyo, 153-8914, Japan.

Received 1 February 2008; Accepted (in revised version) 19 June 2008
Available online 29 September 2008

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.

AMS subject classifications: 35R30 (35K20)

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Key words: Point source, source identification, heat equations, noisy data, convergence.

*Corresponding author.
Email: lling@hkbu.edu.hk (L. Ling), take@ms.u-tokyo.ac.jp (T. Takeuchi)
 

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