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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.

MSC:

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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References:

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