Portugaliae Mathematica


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Volume 72, Issue 2-3, 2015, pp. 247–266
DOI: 10.4171/PM/1967

Published online: 2015-07-23

Spectral analysis in thin tubes with axial heterogeneities

Rita Ferreira[1], M. Luísa Mascarenhas[2] and Andrey Piatnitski

(1) King Abdullah University of Science and Technology (KAUST), Thuwal, Saudi Arabia
(2) Universidade Nova de Lisboa, Caparica, Portugal

In this paper, we present the 3D-1D asymptotic analysis of the Dirichlet spectral problem associated with an elliptic operator with axial periodic heterogeneities. We extend to the 3D-1D case previous 3D-2D results (see [10]) and we analyze the special case where the scale of thickness is much smaller than the scale of the heterogeneities and the planar coefficient has a unique global minimum in the periodic cell. These results are of great relevance in the comprehension of the wave propagation in nanowires showing axial heterogeneities (see [17]).

Keywords: Spectral analysis, dimension reduction, homogenization, quantum waveguides

Ferreira Rita, Mascarenhas M. Luísa, Piatnitski Andrey: Spectral analysis in thin tubes with axial heterogeneities. Port. Math. 72 (2015), 247-266. doi: 10.4171/PM/1967