Effects of Rayleigh waves on the essential spectrum in perturbed doubly periodic elliptic problems
Analysis of PDEs
2017-08-14 v2 Mathematical Physics
math.MP
Spectral Theory
Abstract
We give an example of a scalar second order differential operator in the plane with double periodic coefficients and describe its modification, which causes an additional spectral band in the essential spectrum. The modified operator is obtained by applying to the coefficients a mirror reflection with respect to a vertical or horizontal line. This change gives rise to Rayleigh type waves localized near the line. The results are proven using asymptotic analysis, and they are based on high contrast of the coefficient functions.
Keywords
Cite
@article{arxiv.1604.02835,
title = {Effects of Rayleigh waves on the essential spectrum in perturbed doubly periodic elliptic problems},
author = {F. L. Bakharev and G. Cardone and S. A. Nazarov and J. Taskinen},
journal= {arXiv preprint arXiv:1604.02835},
year = {2017}
}
Comments
14 pages, 3 figures