Some results in homogenization tackling memory effects

We give some results on homogenization of transport equations involving transverse and time-dependent oscillating coefficients. For this purpose, we adapt the results of Tartar, which enable to deduce the effective equations. These latter involve memory kernels, as expected, which are described in terms of pseudodifferential operators. Other types of partial differential equations are also dealt with here, which all involve first-order time derivatives.