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

Abstract

We study the homogenization of a parabolic equation with oscillations in both space and time in the coefficient a(x/ε,t/ε2) in the elliptic part and spatial oscillations in the coefficient ρ(x/ε) that is multiplied with the time derivative ∂tuε. 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/ε2) and disappears if either of these oscillations is removed.