Projects per year
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.
23/07/14 → 22/06/19
Project: Research council
Cherednichenko, K., Ershova, Y., & Kiselev, A. (2020). Effective behaviour of critical-contrast PDEs: micro-resonances, frequency conversion, and time dispersive properties. I. Communications in Mathematical Physics, 375(3), 1833-1884. https://doi.org/10.1007/s00220-020-03696-2