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Numerical solution of the inverse problem of determining an unknown source term in a heat equation. (English) Zbl 0994.65100
Summary: A numerical procedure for an inverse problem of identification of an unknown source in a heat equation is presented. Approach of proposed method is to approximate unknown function by polygons linear pieces which are determined consecutively from the solution of minimization problem based on the overspecified data. Numerical examples are presented.

MSC:
65M32Inverse problems (IVP of PDE, numerical methods)
65M06Finite difference methods (IVP of PDE)
35K05Heat equation
35R30Inverse problems for PDE
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References:
[1] Cannon, J. R.; Duchateau, P.: Structural identification of an unknown source term in a heat equation. Inverse problems 14, 535-551 (1998) · Zbl 0917.35156
[2] O.A. Ladyzhenskaya, V.A. Solonnikov, N.N. Uralceva, Linear and Quasilinear Equations of Parabolic Type, Nauka, Moscow, 1967 (in Russian).
[3] M. Pilant, W. Rundell, Undetermined coefficient problems for quasilinear parabolic equations, in: Proceedings of the Conference on Inverse Problems in Partial Differential Equation, Arcata, California, 29 July--4 August 1989. · Zbl 0687.65110
[4] Duchateau, P.; Rundell, W.: Unicity in an inverse problem for an unknown reaction term in a reaction-diffusion equation. J. diff. Eq. 59, 155-164 (1985) · Zbl 0564.35097