Diffusion through a composite medium with a semi-periodic structure and high contrasting diffusivity
Résumé
We address the homogenization of the stationary diffusion equation in a composite medium with two components M-epsilon and B-epsilon having respectively A(epsilon)(x) and alpha(epsilon)A(epsilon)(x) as diffusivity coefficients. We assume periodic distribution with size epsilon of the "holes" B-epsilon but no periodicity is assumed on the matrices A(epsilon). The high contrast between the two components is characterized by the assumption that the sequence alpha(epsilon) decreases towards zero. We study the three regimes corresponding to the limits alpha := lim(epsilon -> 0) alpha(epsilon)/epsilon. It is shown in particular that in the case alpha = 0, the inclusions B-epsilon behave as holes on the macroscopic diffusion process.