Diffusion through a composite structure with a high contrasting diffusivity

Article type: Research Article

Authors: Sili, Ali

Affiliations: Institut de Mathématiques de Marseille (I2M, UMR 7373), Centre de Mathématiques et Informatique, 39 rue Joliot-Curie, 13453 Marseille cedex 13, France and Département de Mathématiques, Université de Toulon, 83957, La Garde cedex, France. E-mail: [email protected]

Abstract: We consider the stationary diffusion equation in a periodic composite medium made of two components Mε and Bε having very different diffusivity, the ratio between the coefficients of the diffusion in that structure being 1/αε2, where ε is the size of the period and αε which represents the amplitude of the diffusion in the inclusions Bε is a decreasing sequence towards zero. We show that the inclusions Bε work on the macroscopic diffusion as holes. In particular for scalings 0<αε�ε corresponding to very weak diffusion in Bε, the volume fraction of the material at the limit is the well known one in the case of holes.

Keywords: homogenization, high contrast, conductivity, degenerate equation, volume fraction

DOI: 10.3233/ASY-141241

Journal: Asymptotic Analysis, vol. 89, no. 1-2, pp. 173-187, 2014