Localization of eigenfunctions in a thin cylinder with a locally periodic oscillating boundary
Artikel i vetenskaplig tidskrift, 2022

We study a Dirichlet spectral problem for a second-order elliptic operator with locally periodic coefficients in a thin cylinder. The lateral boundary of the cylinder is assumed to be locally periodic. When the thickness of the cylinder ε tends to zero, the eigenvalues are of order ε−2 and described in terms of the first eigenvalue μ(x1) of an auxiliary spectral cell problem parametrized by x1, while the eigenfunctions localize with rate ε.

Dimension reduction

Localization of eigenfunctions

Thin domains

Locally periodic structure

Homogenization

Författare

Klas Pettersson

Chalmers, Mikroteknologi och nanovetenskap, Kvantteknologi, Kvantteknologi

Journal of Mathematical Analysis and Applications

0022-247X (ISSN) 1096-0813 (eISSN)

Vol. 511 1 126074

Ämneskategorier

Beräkningsmatematik

Annan fysik

Matematisk analys

DOI

10.1016/j.jmaa.2022.126074

Mer information

Senast uppdaterat

2022-02-22