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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.
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참고문헌 (25)
참고문헌 신청
A. Hasanov / 2007 / Simultaneous determination of source terms in a linear parabolic problem from the final overdetermination: Weak solution approach / J. Math. Anal. Appl 3
A. Kirsch / 1996 / An Introduction to the Mathematical Theory of Inverse Problems / Springer-Verlag
C. Zheng / 1995 / Applied Contaminant Transport Modelling: Theory and Practice / Van Nostrand Reinhold
D. W. Kim / 2008 / Heat Conduction to Photoresist on Top of Wafer during Post Exposure Bake Process: I. Numerical Approach / Japan. J. Appl. Phys 47 : 8338 ~ 8348
F. Berntsson / 1999 / A spectral method for solving the sideways heat equation / Inverse Problems 15 (4) : 891 ~ 906
A. Kirsch / 1996 / An Introduction to the Mathematical Theory of Inverse Problems / Springer-Verlag
C. Zheng / 1995 / Applied Contaminant Transport Modelling: Theory and Practice / Van Nostrand Reinhold
D. W. Kim / 2008 / Heat Conduction to Photoresist on Top of Wafer during Post Exposure Bake Process: I. Numerical Approach / Japan. J. Appl. Phys 47 : 8338 ~ 8348
F. Berntsson / 1999 / A spectral method for solving the sideways heat equation / Inverse Problems 15 (4) : 891 ~ 906
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