A Strange Term in the Homogenization of Parabolic Equations with Two Spatial and Two Temporal Scales

We study the homogenization of a parabolic equation with oscillations in both space and time in the coefficient a x/ε, t/ε 2 in the elliptic part and spatial oscillations in the coefficient ρ x/ε that is multiplied with the time derivative ∂ t u ε . We obtain a strange term in the local problem. This phenomenon appears as a consequence of the combination of the spatial oscillation in ρ x/ε and the temporal oscillation in a x/ε, t/ε 2 and disappears if either of these oscillations is removed