Inverse problem for a class of two-dimensional diffusion equations with piecewise constant coefficients

In this paper, we consider an inverse problem for a class of two-dimensional diffusion equations with piecewise constant coefficients. This problem is studied using an explicit formula for the relevant spectral measures and an asymptotic expansion of the solution of the diffusion equations. A numeri...

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Bibliographic Details
Published in:Journal of optimization theory and applications 1999, Vol.100 (1), p.29-57
Main Authors: MOCHI, M, PACELLI, G, RECCHIONI, M. C, ZIRILLI, F
Format: Article
Language:English
Subjects:
Exact sciences and technology
Inverse problems
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Partial differential equations, miscellaneous problems
Sciences and techniques of general use
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Summary:In this paper, we consider an inverse problem for a class of two-dimensional diffusion equations with piecewise constant coefficients. This problem is studied using an explicit formula for the relevant spectral measures and an asymptotic expansion of the solution of the diffusion equations. A numerical method that reduces the inverse problem to a sequence of nonlinear least-square problems is proposed and tested on synthetic data.
ISSN:0022-3239
1573-2878
DOI:10.1023/A:1021712830465