G. Allaire et C. Conca, ASYMPTOTIC ANALYSIS OF THE WAVE-EQUATION SPECTRUM - BLOCH WAVE HOMOGENIZATION, Comptes rendus de l'Academie des sciences. Serie 1, Mathematique, 321(3), 1995, pp. 293-298
This Note is devoted to the study of the asymptotic behaviour of the s
pectrum of the wave equation in a periodic heterogeneous medium as its
period goes to zero. We introduce a method of Bloch wave homogenizati
on that yields a characterization of part of the spectrum concentratin
g near the origin, which cannot be obtained by classical homogenizatio
n 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.