Homogenization of parabolic equations with contrasting coefficients

We consider non-stationary diffusion problems in a periodic medium with inclusions filled with a material of small conductivity. We propose homogenized equations whose solutions approximate those of the problems under consideration. We prove estimates for the accuracy of this approximation as the period of the medium and the conductivity coefficient tend to zero. The form of the homogenized equations and the accuracy estimates depend essentially on the asymptotic behaviour of the conductivity coefficient in relation to the square of the period.