Geodesic
Diffusion and Laplacian transport for absorbing domains
Nanosistemy: fizika, himiâ, matematika, Tome 4 (2013) no. 4, pp. 446-466.

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We study (stationary) Laplacian transport by the Dirichlet-to-Neumann formalism. Our results concern a formal solution of the geometrically inverse problem for localisation and reconstruction of the form of absorbing domains. Here, we restrict our analysis to the one- and two-dimensional cases. We show that the last case can be studied by the conformal mapping technique. To illustrate this, we scrutinize the constant boundary conditions and analyze a numeric example.
Keywords: Laplacian transport, dirichlet-to-Neumann operators, conformal mapping. 
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     author = {Ibrahim Baydoun and Valentin A. Zagrebnov},
     title = {Diffusion and {Laplacian} transport for absorbing domains},
     journal = {Nanosistemy: fizika, himi\^a, matematika},
     pages = {446--466},
     publisher = {mathdoc},
     volume = {4},
     number = {4},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/NANO_2013_4_4_a0/}
}
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Ibrahim Baydoun; Valentin A. Zagrebnov. Diffusion and Laplacian transport for absorbing domains. Nanosistemy: fizika, himiâ, matematika, Tome 4 (2013) no. 4, pp. 446-466. http://geodesic.mathdoc.fr/item/NANO_2013_4_4_a0/