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

Authors
Mochi, M Pacelli, G Recchioni, MC Zirilli, F
Citation
M. Mochi et al., Inverse problem for a class of two-dimensional diffusion equations with piecewise constant coefficients, J OPTIM TH, 100(1), 1999, pp. 29-57
Citations number
18
Categorie Soggetti
Engineering Mathematics
Journal title
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
ISSN journal
00223239 → ACNP
Volume
100
Issue
1
Year of publication
1999
Pages
29 - 57
Database
ISI
SICI code
0022-3239(199901)100:1<29:IPFACO>2.0.ZU;2-A
Abstract
In this paper, we consider an inverse problem for a class of two-dimensiona l diffusion equations with piecewise constant coefficients. This problem is studied using an explicit formula for the relevant spectral measures and a n asymptotic expansion of the solution of the diffusion equations. A numeri cal method that reduces the inverse problem to a sequence of nonlinear leas t-square problems is proposed and tested on synthetic data.