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Inverse Problem for a Class of Two-Dimensional Diffusion Equations with Piecewise Constant Coefficients |
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| Authors: | Mochi M. Pacelli G. Recchioni M. C. Zirilli F. |
| Affiliation: | (1) Via del Gelsomino 86, Rome, Italy;(2) Institute of Mathematics and Statistics, University of Ancona, Ancona, Italy;(3) Institute of Mathematics and Statistics, University of Ancona, Ancona, Italy;(4) Department of Mathematics, University of Rome !["ldquo"]("/content/n810256767h2jtg5/xlarge8220.gif") La Sapienza!["rdquo"]("/content/n810256767h2jtg5/xlarge8221.gif") , Rome, Italy |
| Abstract: | 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. |
| Keywords: | Inverse problems diffusion equations spectral measures asymptotic expansions nonlinear least squares |
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