Memory Effects and Gamma-Convergence: a Time-Dependent Case

We study the asymptotic behaviour of the energy functional associated to a parametric first order, nonlinear ordinary differential equation. Techniques of Young measures are improved in order to characterize the Γ-limit of the sequence of energy functionals in terms of the oscillations of the coefficients. Some sort of independence between time and the oscillating character of the coefficients is assumed. The example of a periodic mixture of two materials with coefficients analytic in time is presented