Work

Localization of Eigenfunctions of the Dirichlet Problem Near a Contour at the Boundary of a Thin Domain

Year: 2024

Type: article

Abstract: We consider the spectral Dirichlet problem for the Laplace operator in a thin three-dimensional domain of a variable thickness which admits a maximum value at a smooth closed contour either inside the longitudinal cross-section, or at its boundary. We find out asymptotic expansions of the eigenvalues which involve eigenvalues of the harmonic oscillator at the axis or the half-axis as well as of a certain second order ordinary differential equation at the contour. The eigenfuctions are localized in the vicinity of the contour.

Source: Дифференциальные уравнения

DOI: 10.31857/s0374064124120073

Author: S. A. Nazarov

Institution: Institute of Problems of Mechanical Engineering

Language: English

Topic: Spectral Theory in Mathematical Physics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funder: Ministry of Science and Higher Education of the Russian Federation

Award: G6036601041