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Published online: 2015-07-23
Spectral analysis in thin tubes with axial heterogeneitiesRita Ferreira, M. Luísa Mascarenhas 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 ) 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 ).
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