Simultaneous space diffusivity and source term reconstruction in 2D IHCP. (English) Zbl 1005.65106

The authors discuss the simultaneous estimation of the diffusivity coefficient and source term, together with the temperature and the heat flux in the two dimensional IHCP, provided that Cauchy data at the active boundary and the initial temperature distributions are given approximately. They assume that the source term can be written in the form \(f(x,y) g(t) \), or that the source term is independent of time, and they develop a table numerical marching scheme bases on discrete mollification for recovering the diffusivity coefficients and source terms. The stability of the scheme and its error analysis are discussed. Several interesting numerical examples are presented.


65M32 Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs
35R30 Inverse problems for PDEs
35K15 Initial value problems for second-order parabolic equations
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[1] Ewing, R.; Lin, T., Parameter identification problems in single-phase and two-phase flow, (), 85-108
[2] Ewing, R.; Lin, T., A note on source term identification for parabolic equations, (), 263-281
[3] Mejía, C.E.; Murio, D.A., Mollified hyperbolic method for coefficient identification problems, Computers math. applic., 26, 5, 1-12, (1993) · Zbl 0789.65090
[4] Murio, D.A., The mollification method and the numerical solution of ill-posed problems, (1993), John Wiley New York
[5] Coles, C.; Murio, D.A., Identification of parameters in the 2-D IHCP, Computers math. applic., 40, 939-956, (2000) · Zbl 0961.65085
[6] Craven, P.; Wahba, G., Smoothing noisy data with spline functions, Numer. math., 31, 377-403, (1979) · Zbl 0377.65007
[7] Wahba, G., Spline models for observational data, CBMS-NSF regional conferences series in applied mathematics, (1990), SIAM Philadephia, PA · Zbl 0813.62001
[8] Zhan, S.; Coles, C.; Murio, D.A., Automatic numerical solution of the generalized 2-D IHCP by discrete mollification, Computers math. applic., 41, 1/2, 15-38, (2001) · Zbl 0983.65109
[9] Murio, D.A.; Mejía, C.E.; Zhan, S., Discrete mollification and automatic numerical differentiation, Computers math. applic., 35, 5, 1-16, (1998) · Zbl 0910.65010
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