References
- Ladyzhenskaya, OA, 1985. Boundary Value Problems in Mathematical Physics. New York: Springer Verlag; 1985.
- DuChateau, P, 1995. Monotonicity and invertibility of coefficient-to-data mappings for parabolic inverse problems, SIAM J. Math. Anal. 26 (1995), pp. 1473–1487.
- DuChateau, P, 1996. "Introduction to inverse problems in partial differential equations for engineers, physicists and mathematicians". In: Gottlieb, J, and DuChateau, P, eds. Parameter Identification and Inverse Problems in Hydrology, Geology and Ecology. Dordrecht: Kluwer Academic Publishers; 1996. pp. 3–38.
- DuChateau, P, Thelwell, R, and Butters, G, 2004. Analysis of an adjoint problem approach to the identification of an unknown diffusion coefficient, Inverse Probl. 20 (2004), pp. 601–625.
- Hasanov, A, DuChateau, P, and Pektas, B, 2006. An adjoint problem approach and coarse-fine mesh method for identification of the diffusion coefficient in a linear parabolic equation, J. Inverse Ill-Posed Probl. 14 (5) (2006), pp. 435–463.
- Hasanov, A, 2007. Simultaneous determination of source terms in a linear parabolic problem from the final overdetermination: Weak solution approach, J. Math. Anal. Appl. 330 (2007), pp. 766–779.
- Hasanov, A, Demir, A, and Erdem, A, 2007. Monotonicity of input–output mappings in inverse coefficient and source problems for parabolic equations, J. Math. Anal. Appl. 335 (2007), pp. 1434–1451.
- Kabanikhin, SI, Hasanov, A, and Penenko, AV, 2008. A gradient descent method for solving an inverse coefficient heat conduction problem, Numerical Anal. Appl. 1 (1) (2008), pp. 34–45.
- Ivanov, VK, Vasin, VV, and Tanana, VP, 1978. Theory of Linear Ill-Posed Problems and Its Applications. Nauka, Moscow. 1978.
- Chavent, G, and Lemonnier, P, 1974. Identification de la non-linearite d'une equation parabolique quasilinearie, Appl. Math. Optim. 1 (1974), pp. 121–162.
- Jarny, Y, Ozisik, MN, and Bardon, JP, 1991. A general optimization method using adjoint equation for solving multidimensional inverse heat conduction, Int. J. Heat Mass Transfer 34 (1991), pp. 2911–2918.
- Knabner, P, and Bitterlilich, S, 2002. An efficient method for solving an inverse problem for the Richards equation, J. Comput. Appl. Math. 147 (2002), pp. 153–173.
- Nabakov, R, 1996. "An inverse problem for porous medium equation". In: Gottlieb, J, and DuChateau, P, eds. Parameter Identification and Inverse Problems in Hydrology, Geology and Ecology. Dordrecht: Kluwer Academic Publishers; 1996. pp. 155–163.
- Cannon, JR, and DuChateau, P, 1987. Design of an experiment for the determination of a coefficient in a nonlinear diffusion equation, Int. J. Eng. Sci. 25 (1987), pp. 1067–1078.
- Hanke, M, and Scherzer, O, 1999. Error analysis of an equation error method for the identification of the diffusion coefficient in a quasilinear parabolic differential equation, SIAM J. Appl. Math. 59 (1999), pp. 1012–1027.
- Reeve, DE, and Spivack, M, 1999. Recovery of a variable coefficient in a coastal evolution equation, J. Comput. Phys. 151 (1999), pp. 585–596.
- Richter, GR, 1981. Numerical identification of a spatially varying diffusion coefficient, Math. Comput. 36 (1981), pp. 375–386.
- Protter, MH, and Weinberger, HE, 1967. Maximum Principles in Differential Equations. Englewood Cliffs, N.J.: Prentice-Hall; 1967.
- Samarskii, AA, 2001. Theory of Difference Schemes. New York: John Wiley and Sons; 2001.