Work

Asymptotic Expansions for the Transmission Eigenvalues of Periodic Scatterers of Bounded Support

Year: 2026

Type: article

Abstract: We consider the transmission eigenvalues for a bounded scatterer with a periodically varying index of refraction, and derive the first-order corrections to the limiting transmission eigenvalues. We assume the scatterer contrast to be of one sign, in which case the transmission eigenvalue problem can be written in terms of operators corresponding to a fourth-order partial differential equation with periodic coefficients. We perform two scale asymptotics for this biharmonic-type homogenization problem and show convergence estimates, which require a boundary corrector function, and this boundary corrector function appears in the formula for the transmission eigenvalues correction.

Source: Asymptotic Analysis

DOI: 10.1177/09217134251407492

Authors: Fioralba Cakoni, Shari Moskow

Institutions: Rutgers, The State University of New Jersey, Drexel University

Language: English

Topic: Advanced Mathematical Modeling in Engineering

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funder: Division of Mathematical Sciences

Awards: G1402688964, G1795131396, G4701449825