Diffusion through a composite medium with a semi-periodic structure and high contrasting diffusivity

Article type: Research Article

Authors: Sili, Ali^{a; b}

Affiliations: [a] Institut de Mathématiques de Marseille, I2M, UMR 7373, CMI, 39 rue Joliot Curie, 13453 Marseille, France. E-mail: [email protected] | [b] Département de Mathématiques, Université de Toulon, 83957 La Garde Cedex, France

Abstract: We address the homogenization of the stationary diffusion equation in a composite medium with two components Mε and Bε having respectively Aε(x) and αεAε(x) as diffusivity coefficients. We assume periodic distribution with size ε of the “holes” Bε but no periodicity is assumed on the matrices Aε. The high contrast between the two components is characterized by the assumption that the sequence αε decreases towards zero. We study the three regimes corresponding to the limits α:=limε→0αεε. It is shown in particular that in the case α=0, the inclusions Bε behave as holes on the macroscopic diffusion process.

Keywords: homogenization, high contrast, conductivity, degenerate equation, semi-periodic structure

DOI: 10.3233/ASY-161370

Journal: Asymptotic Analysis, vol. 98, no. 4, pp. 309-324, 2016