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Zbl 0926.35160
Gryazin, Yuriy A.; Klibanov, Michael V.; Lucas, Thomas R.
Imaging the diffusion coefficient in a parabolic inverse problem in optical tomography. (English)
[J] Inverse Probl. 15, No.2, 373-397 (1999). ISSN 0266-5611

Summary: The elliptic systems method, previously developed by the second and third authors, is extended to the reconstruction of the diffusion coefficient of an inverse problem for the parabolic equation $u_t= \text{div}(D(x)\nabla u)$ in the $n$-dimensional case $(n= 2,3)$. This inverse problem has applications to optical imaging of small abnormalities hidden in a random media, such as biological tissues, foggy atmospheres, murky water, etc. Results of numerical experiments are presented in the two-dimensional case, for realistic ranges of the parameters.

MSC 2000:: *35R30 Inverse problems for PDE
35K15 Second order parabolic equations, initial value problems
92C55 Tomography

Keywords: reconstruction of the diffusion coefficient; optical imaging of small abnormalities hidden in a random media, such as biological tissues, foggy atmospheres, murky water

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