The appearance of memory effects for a conservative system (Q1627428)

In the late 1980, Tartar studied a problem \[ \frac{\partial u_n}{\partial t}+a_nu_n=f\quad\text{in }\Omega\times(0,T), \quad u_n|_{t=0}=v\quad\text{in }\Omega \] for a sequence \(a_n\) converging weakly in \(L^\infty(\Omega)\). In order to tackle unphysical properties of this model, the present paper adapts and generalizes some results to conservative systems and a sequence of differential equations which in the limit gives an effective equation with a memory effect: The main result is obtained under more realistic assumptions concerning the oscillations of the initial data and the coefficients.