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NANOSYSTEMS: PHYSICS, CHEMISTRY, MATHEMATICS, 2013, 4 (4), P. 446–466

DIFFUSION AND LAPLACIAN TRANSPORT FOR ABSORBING DOMAINS

Ibrahim Baydoun – École Centrale Paris, ib_baydoun1985@hotmail.com
Valentin A. Zagrebnov – Avenue Sully Prudhomme, 92290 Chtenay-Malabry, France; Département de Mathématiques Université d’ Aix-Marseille, Laboratoire d’ Analyse, Topologie et Probabilités (UMR 7353), CMI Technopôle Château-Gombert, 39, rue F. Joliot Curie, 13453 Marseille Cedex 13, France; Valentin.Zagrebnov@univ-amu.fr

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.

PACS 47A55, 47D03, 81Q10

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