ASYMPTOTIC ANALYSIS OF THE WAVE-EQUATION SPECTRUM - BLOCH WAVE HOMOGENIZATION

This Note is devoted to the study of the asymptotic behaviour of the spectrum of the wave equation in a periodic heterogeneous medium as its period goes to zero. We introduce a method of Bloch wave homogenization that yields a characterization of part of the spectrum concentrating near the origin, which cannot be obtained by classical homogenization methods. This part of the spectrum, the so-called Bloch spectrum, is made of limits of renormalized sequences of eigenvalues of the order of the square of the medium period.