Evgeni Korotyaev
The Propagation of the Waves in Periodic Media at Large Time
The paper is published: Asymptotic Anal., 15, 1 (1997), 1-24

MSC:

35L05 Wave equation

35J10 Schrodinger operator, See also {35Pxx}

Abstract: Asymptotics at large time of the Green
function to the
wave equation with periodic coefficients are found.
A particular attention is given to its asymptotics near the wave front.
It is shown that
the spectral band (with number $n=0, 1, 2,..$) of the corresponding
Hill operator is associated with a wave having the front velocity $c_n < 1 $.
Estimates for $c_n$ in the terms of the gap lengths, the effective masses
of the Hill operator are
proved (both with fixed number $n$ and their sums).
Some extensions for more general cases ( the Dirac operator with
periodic coefficients, the Schrodinger operator with finite band potentials
etc.) are also obtained.


Keywords: wave equation, Hill operator, effective mass