Diffusion and laplacian transport for absorbing domains
Abstract
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.
Supporting agencies: During his visit of Indiana University- Purdue University Indianapolis, V.A.Z. benefited of numerous useful suggestions and comments concerning the present paper from discussions with Pavel Bleher. V.A.Z is most grateful Pavel Bleher and Department of Mathematical Sciences of IUPUI for kind invitation and for warm hospitality extended him at the Indiana University (Indianapolis).
About the Authors
I. BaydounFrance
Ibrahim Baydoun
Ecole Centrale Paris 2 Avenue Sully Prudhomme, 92290 Chtenay-Malabry
V. A. Zagrebnov
Departement de Mathematiques- Universite d’Aix-Marseille
France
France
Valentin A. Zagrebnov
Laboratoire d’Analyse, Topologie et Probabilites (UMR 7353)
CMI-Technopole Chateau-Gombert, 39, rue F. Joliot Curie, 13453 Marseille Cedex 13
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Review
For citations:
Baydoun I., Zagrebnov V.A. Diffusion and laplacian transport for absorbing domains. Nanosystems: Physics, Chemistry, Mathematics. 2013;4(4):446-466.
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