Homogenization of the Neumann problem in a domain a part of which is a set of channels (Q1874767)

The author studies the asymptotic behaviour of the solution of the Neumann problem in a domain partially formed by channels of radius and length depending on \(\varepsilon\) (\(\varepsilon\) is a small parameter). The channels are assumed to be arranged \(\varepsilon\)-periodically. The problem is solved by new techniques which permit to estimate the closedness of solutions of the original and limit problems as well as the closedness of solutions of the corresponding spectral problems and study similar problems for higher-order equations.