NUMERICAL METHODS FOR RECONSTRUCTION OF THE SOURCE TERM OF HEAT EQUATIONS FROM THE FINAL OVERDETERMINATION
1
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
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.
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.
참고문헌 (25)
- S. Attaway, "Matlab: A Practical Introduction to Programming and Problem Solving" (2009), Elsevier
- J. Bear, "Dynamics of Fluids in Porous Media" (1972), Elsevier
- F. Berntsson, "A spectral method for solving the sideways heat equation", Inverse Problems, 15(4), pp.891~906 (1999)
- I. Bushuyev, "Global uniqueness for inverse parabolic problems with final observation", Inverse Problems, 11(4), pp.L11~L16 (1995)
- J. R. Cannon, "An inverse problem for an unknown source in a heat equation", J. Math. Anal. Appl, 75(2), pp.465~485 (1980)
- J. R. Cannon, "Structural identification of an unknown source term in a heat equation", Inverse Problems, 14(3), pp.535~551 (1998)
- M. Choulli, "An inverse problem for a semilinear parabolic equation", Inverse Problems, 10(5), pp.1123~1132 (1994)
- M. Choulli, "Generic well-posedness of an inverse parabolic problem-the Holder-space approach", Inverse Problems, 12(3), pp.195~205 (1996)
- Y. J. Deng, "Iteration methods on sideways parabolic equations", Inverse Problems, 25(9), pp.095004~ (2009)
- Y. J. Deng, "New fast iteration for determining surface temperature and heat flux of general sideways parabolic equation", Nonlinear Anal. Real World Appl, 12, pp.156~166 (2011)
- L. Elden, "Wavelet and Fourier methods for solving the sideways heat equation", SIAM J. Sci. Comput, 21(6), pp.2187~2205 (2000)
- H. W. Engl, "Regularization of Inverse Problems" (1996), Kluwer Academic Publishers
- L. Evans, "Partial Differential Equations" (1998), American Mathematical Society
- A. Hasanov, "Simultaneous determination of source terms in a linear parabolic problem from the final overdetermination: Weak solution approach", J. Math. Anal. Appl, 330(2), pp.766~779 (2007)
- M. I. Ivanchov, "The inverse problem of determining the heat source power for a parabolic equation under arbitrary boundary conditions", J. Math. Sci, 88(3), pp.432~436 (1998)
- D. W. Kim, "Heat Conduction to Photoresist on Top of Wafer during Post Exposure Bake Process: I. Numerical Approach", Japan. J. Appl. Phys, 47, pp.8338~8348 (2008)
- A. Kirsch, "An Introduction to the Mathematical Theory of Inverse Problems" (1996), Springer-Verlag
- L. Ling, "Identification of source locations in twodimensional heat equations", Inverse Problems, 22(4), pp.1289~1305 (2006)
- J. Liu, "A modified landweber iteration for general sideways parabolic equations", Acta Math. Appl. Sin. Engl. Ser, 27(4), pp.727~738 (2011)
- V. A. Morozov, "On the solution of functional equations by the method of regularization", Soviet Math. Dokl, 7, pp.414~417 (1966)
- G. Ozkum, "On the Inverse Problem of the Fractional Heat-Like Partial Differential Equations: Determination of the Source Function", Adv. Math. Phys, 2013, pp.8~ (2013)
- M. Renardy, "Mathematical Problems in Viscoelasticity" (1987), Wiley
- G. M. Vainikko, "Iteration Procedures in Ill-Posed Problems" (1986), Nauka (in Russian) McCormick, S.F
- R. H. S. Winterton, "Heat Transfer" (1997), Oxford University Press
- C. Zheng, "Applied Contaminant Transport Modelling: Theory and Practice" (1995), Van Nostrand Reinhold