[1] Wang Zewen,. Determination of pollution point source in parabolic system model [J]. Journal of Southeast University (English Edition), 2009, 25 (2): 278-285. [doi:10.3969/j.issn.1003-7985.2009.02.029]

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Determination of pollution point source in parabolic system model()

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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:

25

Issue:

2009 2

Page:

278-285

Research Field:

Mathematics, Physics, Mechanics

Publishing date:

2009-06-30

Info

Title:

Determination of pollution point source in parabolic system model

Author(s):

Wang Zewen

Department of Mathematics, Southeast University, Nanjing 210096, China
School of Mathematics and Informational Science, East China Institute of Technology, Fuzhou 344000, China

Keywords:

inverse source problem;  parabolic system;  uniqueness;  local Lipschitz stability;  pollution source

PACS:

O175.24

DOI:

10.3969/j.issn.1003-7985.2009.02.029

Abstract:

This paper considers an inverse problem for a partial differential equation to identify a pollution point source in a watershed.The mathematical model of the problem is a weakly coupled system of two linear parabolic equations for the concentrations u(x, t)and v(x, t)with an unknown point source F(x, t)=λ(t)δ(x-s)related to the concentration u(x, t), where s is the point source location and λ(t)is the amplitude of the pollution point source.Assuming that source F becomes inactive after time T^*, it is proved that it can be uniquely determined by the indirect measurements {v(0, t), v(a, t), v(b, t), v(l, t), 0<t≤T, T^*<T}, and, thus, the local Lipschitz stability for this inverse source problem is obtained.Based on the proof of its uniqueness, an inversion scheme is presented to determine the point source.Finally, two numerical examples are given to show the feasibility of the inversion scheme.

References:

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Memo

Memo:

Biography: Wang Zewen(1974—), male, graduate, associate professor, zwwang@ecit.edu.cn.
Foundation items: The National Natural Science Foundation of China(No.10861001), the Natural Science Foundation of Jiangxi Province.
Citation: Wang Zewen.Determination of pollution point source in parabolic system model[J].Journal of Southeast University(English Edition), 2009, 25(2):278-285.

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