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Journal Articles Zeitschrift für Angewandte Mathematik und Physik Year : 2013

Waveguide with non-periodically alternating Dirichlet and Robin conditions: homogenization and asymptotics

Abstract

We consider a magnetic Schrödinger operator in a planar infinite strip with frequently and non-periodically alternating Dirichlet and Robin boundary conditions. Assuming that the homogenized boundary condition is the Dirichlet or the Robin one, we establish the uniform resolvent convergence in various operator norms and we prove the estimates for the rates of convergence. It is shown that these estimates can be improved by using special boundary correctors. In the case of periodic alternation, pure Laplacian, and the homogenized Robin boundary condition, we construct two-terms asymptotics for the first band functions, as well as the complete asymptotics expansion (up to an exponentially small term) for the bottom of the band spectrum. Mathematics Subject Classification(2010). 35B27 · 35J15 · 35P05.

Dates and versions

hal-01283613 , version 1 (05-03-2016)

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Denis Borisov, Renata Bunoiu, Giuseppe Cardone. Waveguide with non-periodically alternating Dirichlet and Robin conditions: homogenization and asymptotics. Zeitschrift für Angewandte Mathematik und Physik, 2013, 64 (3), pp.439-472. ⟨10.1007/s00033-012-0264-2⟩. ⟨hal-01283613⟩
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