TY - JOUR
T1 - Effective behaviour of critical-contrast PDEs:
T2 - micro-resonances, frequency conversion, and time dispersive properties. I.
AU - Cherednichenko, Kirill
AU - Ershova, Yulia
AU - Kiselev, Alexander
PY - 2020/2/21
Y1 - 2020/2/21
N2 - 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.
AB - 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.
U2 - 10.1007/s00220-020-03696-2
DO - 10.1007/s00220-020-03696-2
M3 - Article
JO - Communications in Mathematical Physics
JF - Communications in Mathematical Physics
SN - 0010-3616
ER -