Identification of source locations in two-dimensional heat equations

Leevan LING*, Masahiro Yamamoto, Y. C. Hon, Tomoya Takeuchi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

105 Citations (Scopus)

Abstract

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.

Original languageEnglish
Article number011
Pages (from-to)1289-1305
Number of pages17
JournalInverse Problems
Volume22
Issue number4
DOIs
Publication statusPublished - 1 Aug 2006

Scopus Subject Areas

  • Theoretical Computer Science
  • Signal Processing
  • Mathematical Physics
  • Computer Science Applications
  • Applied Mathematics

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