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Original Articles

Identifying an unknown source term in a heat equation

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Pages 901-913 | Received 01 Jun 2008, Accepted 18 Oct 2008, Published online: 16 Sep 2009

References

  • Cannon, JR, 1984. One Dimensional Heat Equation. California: Addison-Wesley Publishing Company; 1984.
  • Savateev, EG, 1995. On problems of determining the source function in a parabolic equation, J. Inv. Ill-posed Probl. 3 (1995), pp. 83–102.
  • Solov'ev, VV, 1990. Solvability of the inverse problem of finding a source, using overdetermination on the upper base for a parabolic equation, Diff. Equ. 25 (1990), pp. 1114–1119.
  • Cannon, JR, and Estevz, SP, 1986. An inverse problem for the heat equation, Inverse Probl. 2 (1986), pp. 395–403.
  • Li, GS, and Yamamoto, M, 2006. Stability analysis for determining a source term in a 1-D advection-dispersion equation, J. Inv. Ill-posed Probl. 14 (2006), pp. 147–155.
  • Yamamoto, M, 1993. Condtional stability in determation of force terms of heat equations in a rectangle, Math. Comput. Model. 18 (1993), pp. 79–88.
  • Buryki, AA, and Denisov, AM, 1997. Determination of the unknown sources in the heat-conduction equation, Comput. Math. Model. 8 (1997), pp. 309–313.
  • Farcas, A, and Lesnic, D, 2006. The boundary-element method for the determination of a heat source dependent on the variable, J. Eng. Math. 54 (2006), pp. 375–388.
  • Johansson, T, and Lesnic, D, 2007. Determination of a spacewise dependent heat source, J. Comput. Appl. Math. 209 (2007), pp. 66–80.
  • Ling, L, Yamamoto, M, Hon, YC, and Takeuchi, T, 2006. Indentification of source locations in two-demensional heat equations, Inverse Probl. 22 (2006), pp. 1289–1305.
  • Ryaben'kii, VS, Tsynov, SV, and Utyuzhnikov, SV, 2007. Inverse source problem and active shielding for composite domains, Appl. Math. Lett. 20 (2007), pp. 511–515.
  • Yi, Z, and Murio, DA, 2004. Source Term identification in 1-D IHCP, Comput. Math. Appl. 47 (2004), pp. 1921–1933.
  • Trong, DD, Long, NT, and Alain, PND, 2005. Nonhomogeneous heat equation: Identification and regularization for the inhomogeneous term, J. Math. Anal. Appl. 312 (2005), pp. 93–104.
  • Lattès, R, and Lions, JL, 1969. The method of quasi-reversibility: Applications to partial differential equations. New York: Elsevier; 1969.
  • Dorroh, JR, and Ru, XP, 1999. The application of the method of quasi-reversibility to the sideways heat equation, J. Math. Anal. Appl. 236 (1999), pp. 503–519.
  • Eldén, L, 1987. Approximations for a Cauchy problem for the heat equation, Inverse Probl. 3 (1987), pp. 263–273.
  • Xiong, XT, Fu, CL, and Qian, Z, 2006. Two numerical methods for solving a backward heat conduction problem, Appl. Math. Comput. 179 (2006), pp. 370–377.
  • Qian, Z, Fu, CL, and Xiong, XT, 2006. Fourth-order modified method for the Cauchy problem for the Laplace equation, J. Comput. Appl. Math. 192 (2006), pp. 205–218.
  • Engl, HW, Hanke, M, and Newbauer, A, 1996. Regularization of Inverse Problems. Boston, MA: Kluwer Academic; 1996.
  • Kirsch, A, 1999. An Introduction to the Mathematical Theory of Inverse Problems. Berlin: Springer; 1999.
  • Landweber, L, 1951. An iteration formula for Fredholm integral equation of the first kind, Am. J. Math. 73 (1951), pp. 615–624.
  • Tautenhahn, U, 1998. Optimality for ill-posed problems under general source conditions, Numer. Funct. Anal. Optimiz. 19 (1998), pp. 377–398.
  • Qian, Z, 2008. Regularization of inverse problems in mathematical physics, Ph.D. diss.. Lanzhou University; 2008.
  • Eldén, L, 1997. Solving an inverse heat conduction problem by ‘Method of lines’, Trans. ASME J. Heat Transfer 119 (1997), pp. 913–923.

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