Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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NUMERICAL METHODS FOR RECONSTRUCTION OF THE SOURCE TERM OF HEAT EQUATIONS FROM THE FINAL OVERDETERMINATION

  • DENG, YOUJUN (SCHOOL OF MATHEMATICS AND STATISTICS CENTRAL SOUTH UNIVERSITY) ;
  • FANG, XIAOPING (SCHOOL OF MATHEMATICS AND STATISTICS CENTRAL SOUTH UNIVERSITY) ;
  • LI, JING (DEPARTMENT OF MATHEMATICS CHANGSHA UNIVERSITY OF SCIENCE AND TECHNOLOGY)
  • Received : 2014.07.25
  • Published : 2015.09.30
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Abstract

This paper deals with the numerical methods for the reconstruction of the source term in a linear parabolic equation from final overdetermination. We assume that the source term has the form f(x)h(t) and h(t) is given, which guarantees the uniqueness of the inverse problem of determining the source term f(x) from final overdetermination. We present the regularization methods for reconstruction of the source term in the whole real line and with Neumann boundary conditions. Moreover, we show the connection of the solutions between the problem with Neumann boundary conditions and the problem with no boundary conditions (on the whole real line) by using the extension method. Numerical experiments are done for the inverse problem with the boundary conditions.

Keywords

Acknowledgement

Supported by : NSF

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