References
- Cannon, JR, 1968. Determination of an unknown heat source from overspecified boundary data, SIAM J. Numer. Anal. 5 (1968), pp. 275–286.
- Cannon, JR, and Duchateau, P, 1998. Structural identification of an unknown source term in a heat equation, Inverse Probl. 14 (1998), pp. 535–551.
- Cannon, JR, and Esteva, SP, 1986. An inverse problem for the heat equation, Inverse Probl. 2 (1986), pp. 395–403.
- Duchateau, P, and Rundell, W, 1985. Unicity in an inverse problem for an unknown reaction term in a reation–diffusion-equation, J. Differ. Eqns. 59 (1985), pp. 155–164.
- Hettlich, F, and Rundell, W, 2001. Identification of a discontinuous source in the heat equation, Inverse Probl. 17 (2001), pp. 1465–1482.
- Silva Neto, AJ, and Özisik, MN, 1992. Two-dimensional inverse heat conduction problem of estimating the time-varying strength of a line heat source, J. Appl. Phys. 71 (1992), pp. 5375–5362.
- Rundell, W, 1980. Determination of an unknown non-homogeneous term in a linear partial differential equation fromoverspecified boundary data, Appl. Anal. 10 (1980), pp. 231–242.
- Solov'ev, VV, 1990. Solvability of the inverse problem of finding a source, using overdetermination on the upper base for a parabolic equation, Differ. Eqns. 25 (1990), pp. 1114–1119.
- Gol'dman, NL, 2005. Determination of the right-hand side in a quasilinear parabolic equation with a terminal observation, Differ. Eqns. 41 (2005), pp. 384–392.
- Cannon, JR, and Esteva, SP, 1991. Uniqueness and stability of 3D heat source, Inverse Probl. 7 (1991), pp. 57–62.
- Constales, D, Kacur, J, and Van Keer, R, 2002. Parameter identification by a single injection-extraction well, Inverse Probl. 18 (2002), pp. 1605–1620.
- Dehghan, M, and Tatari, M, 2002. Determination of a control parameter in a one-dimensional parabolic equation using the method of radial basis functions, Math. Comput. Model. 8 (2) (2002), pp. 161–168.
- Farcas, A, and Lesnic, D, 2006. The boundary-element method for the determination of a heat source dependent on one variable, J. Eng. Math. 54 (2006), pp. 247–253.
- Fatullayev, AG, 2002. Numerical solution of the inverse problem of determining an unknown source term in a heat equation, Math. Comput. Simul. 8 (2) (2002), pp. 161–168.
- Li, GS, Ma, YC, and Li, KT, 2003. An inverse parabolic problem for nonlinear source term with nonlinear boundary condition, J. Inverse Ill-posed Probl. 11 (4) (2003), pp. 371–387.
- Mahar, PS, and Datta, B, 2001. Optimal identification of ground-water pollution source and parameter estimate, J. Water Res. Plan. Manage. 127 (1) (2001), pp. 20–29.
- Yi, Z, and Murio, DA, 2004. Source term identification in 1-D IHCP, Comput. Math. Appl. 47 (2004), pp. 1921–1933.
- Yi, Z, and Murio, DA, 2004. Source term identification in 2-D IHCP, Comput. Math. Appl. 47 (2004), pp. 1517–1533.
- Johansson, BT, and Lesnic, D, 2007. Determination of a spacewise dependent heat source, J. Comput. Appl. Math. 209 (2007), pp. 66–80.
- Johansson, BT, and Lesnic, D, 2007. A variational method for identifying a spacewise-dependent heat source, IMA J. Appl. Math. 72 (6) (2007), pp. 748–760.
- Johansson, BT, and Lesnic, D, 2008. A procedure for determining a spacewise dependent heat source and the initial temperature, Appl. Anal. 87 (2008), pp. 265–276.
- Choulli, M, and Yamamoto, M, 2004. Conditional stability in determining a heat source, J. Inverse Ill-posed Probl. 12 (3) (2004), pp. 233–243.
- Li, GS, and Tan, YG, 2005. A conditional stability for an inverse problem arising in groundwater pollution, J. Chin. Univ. 14 (3) (2005), pp. 217–225.
- Berntsson, F, 1999. A spectral method for solving the sideways heat equation, Inverse Probl. 15 (1999), pp. 891–906.
- Tautenhahn, U, 1997. Optimal stable approximations for the sideways heat equation, J. Inverse Ill-posed Probl. 5 (1997), pp. 287–307.
- Abramowitz, M, and Stegun, IA, 1972. Handbook of Mathematical Functions. New York: Dover Publications; 1972.
- Kirsch, A, 1996. An Introduction to the Mathematical Theory of Inverse Problems. New York: Springer; 1996.
- Nair, MT, and Tautenhahn, U, 2004. Lavrentiev regularization for linear ill-posed problems under general source conditions, J. Math. Anal. Appl. 23 (1) (2004), pp. 167–185.
- Cheng, W, Fu, CL, and Qian, Z, 2007. A modified Tikhonov regularization method for a spherically symmetric three-dimensional inverse heat conduction problem, Math. Comput. Simul. 75 (3–4) (2007), pp. 97–112.
- Cheng, W, and Fu, CL, 2009. Two regularization methods for an axisymmetric inverse heat conduction problem, J. Inverse Ill-posed Probl. 17 (2) (2009), pp. 159–172.