Diffusion and Laplacian Transport for Absorbing Domains

Ibrahim Baydoun (1, 2) , Valentin A. Zagrebnov (1, 2)

1 CPT - Centre de Physique Théorique - UMR 6207
2 CPT - Centre de Physique Théorique - UMR 7332

We study (stationary) Laplacian transport by the Dirichlet-to-Neumann formalism. Our results concerns a \textit{formal} solution of the \textit{geometrical} inverse problem for localisation and reconstruction of the form of absorbing domains. Here we restrict our analysis to the one- and two-dimension cases. We show that the last case can be studied by the conformal mapping technique. To illustrate it we scrutinize constant boundary conditions and analyse a numeric example.

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]

Ibrahim Baydoun, Valentin A. Zagrebnov. Diffusion and Laplacian Transport for Absorbing Domains. Theoretical and Mathematical Physics, 2011, 168 (3), pp.1180-1191. ⟨10.1007/s11232-011-0097-8⟩. ⟨hal-00619923v3⟩