Spectral analysis in thin tubes with axial heterogeneities

  • Rita Ferreira

    King Abdullah University of Science and Technology (KAUST), Thuwal, Saudi Arabia
  • M. Luísa Mascarenhas

    Universidade Nova de Lisboa, Caparica, Portugal
  • Andrey Piatnitski

    Narvik University College, Norway


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]).

Cite this article

Rita Ferreira, M. Luísa Mascarenhas, Andrey Piatnitski, Spectral analysis in thin tubes with axial heterogeneities. Port. Math. 72 (2015), no. 2/3, pp. 247–266

DOI 10.4171/PM/1967