English

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