Identification of source locations in two-dimensional heat equations
Identification of source locations in two-dimensional heat equations
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DOI：
10.1088/0266-5611/22/4/011
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发表时间：
2006-08
期刊：
影响因子：
2.1
通讯作者：
Leevan Ling;Masahiro Yamamoto;Y. Hon;Tomoya Takeuchi
中科院分区：
文献类型：
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作者：
Leevan Ling;Masahiro Yamamoto;Y. Hon;Tomoya Takeuchi
在本文中，我们证明了在二维热方程中由散射测量识别未知源位置的唯一性。基于未知源函数是若干已知函数之和的假设，证明了一个测量点足以确定源的个数，三个测量点足以确定所有未知源的位置。为了验证，我们提出了一个数值重建方案，用于恢复未知源的数量和所有源的位置。
In this paper, we show the uniqueness of the identification of unknown source locations in two-dimensional heat equations from scattered measurements. Based on the assumption that the unknown source function is a sum of some known functions, we prove that one measurement point is sufficient to identify the number of sources and three measurement points are sufficient to determine all unknown source locations. For verification, we propose a numerical reconstruction scheme for recovering the number of unknown sources and all source locations.