Effective behaviour of critical-contrast PDEs: micro-resonances, frequency conversion, and time dispersive properties. I
Analysis of PDEs
2020-05-05 v6 Materials Science
Mathematical Physics
math.MP
Abstract
A novel approach to critical-contrast homogenisation for periodic PDEs is proposed, via an explicit asymptotic analysis of Dirichlet-to-Neumann operators. Norm-resolvent asymptotics for non-uniformly elliptic problems with highly oscillating coefficients are explicitly constructed. An essential feature of the new technique is that it relates homogenisation limits to a class of time-dispersive media.
Keywords
Cite
@article{arxiv.1808.03961,
title = {Effective behaviour of critical-contrast PDEs: micro-resonances, frequency conversion, and time dispersive properties. I},
author = {Kirill Cherednichenko and Yulia Ershova and Alexander Kiselev},
journal= {arXiv preprint arXiv:1808.03961},
year = {2020}
}
Comments
40 pages, 1 figure