On homogenization of networks and junctions

Article type: Research Article

Authors: Chechkin, Gregory A.^; | Jikov, Vasili V. | Lukkassen, Dag^; | Piatnitski, Andrey L.^;

Affiliations: Department of Differential Equations, Faculty of Mechanics and Mathematics, Moscow State University, Moscow 119899, Russia E‐mail: chechkin@mech.math.msu.su | Department of Mathematics, Vladimir Pedagogical University, Prosp. Stroiteley 11, Vladimir 600024, Russia E‐mail: zhikov@vgpu.elcom.ru | Narvik University College, Postboks 385, 8505 Narvik, Norway | NORUT Technology Ltd, 8500 Narvik, Norway E‐mail: dl@hin.no | P.N. Lebedev Physical Institute of RAS, Leninski pr. 53, Moscow 117924, Russia E‐mail: andrey@sci.lebedev.ru

Note: [] Corresponding author.

Abstract: In the paper we propose a new approach to the homogenization theory on periodic wire‐networks and junctions, based on singular measures on these structures. We characterize the Sobolev spaces on such constructions and describe the fields of potential and solenoidal (divergence free) vector‐function. Then we compare the effective coefficients obtained for the singular structures and the classical effective coefficients for thin constructions with vanishing thickness, and show that the corresponding diagram is commutative.

Journal: Asymptotic Analysis, vol. 30, no. 1, pp. 61-80, 2002