Homogenization of the Dirac-like system

The homogenization of the Dirac-like system is studied. It generates memory effects. The memory (or nonlocal) kernel is described by the Volterra inte gral equation. When the coefficient is independent of time, the memory kern el can be characterized explicitly in terms of Young's measure. The homogen ized equation can be reformulated in the kinetic form by introducing the ki netic variable. We also characterize the memory kernel when the coefficient is of separable variable.