Homogenisation and spectral convergence of high-contrast convolution type operators

Cherdantsev, Mikhail ORCID: https://orcid.org/0000-0002-5175-5767, Piatnitski, Andrey and Velčić, Igor 2026. Homogenisation and spectral convergence of high-contrast convolution type operators. Journal of Differential Equations 465 , 114247. 10.1016/j.jde.2026.114247

PDF - Published Version Download (2MB)

Abstract

The paper deals with homogenisation problems for high-contrast symmetric convolution-type operators with integrable kernels in media with a periodic microstructure. We adapt the two-scale convergence method to nonlocal convolution-type operators and obtain the homogenisation result both for problems stated in the whole space and in bounded domains with the homogeneous Dirichlet boundary condition. Our main focus is on spectral analysis. We describe the spectrum of the limit two-scale operator and characterise the limit behaviour of the spectrum of the original problem as the microstructure period tends to zero. It is shown that the spectrum of the limit operator is a subset of the limit of the spectrum of the original operator, and that they need not coincide.

Item Type:	Article
Date Type:	Published Online
Status:	Published
Schools:	Schools > Mathematics
Additional Information:	License information from Publisher: LICENSE 1: URL: http://creativecommons.org/licenses/by/4.0/, Start Date: 2026-02-20
Publisher:	Elsevier
ISSN:	0022-0396
Date of First Compliant Deposit:	3 March 2026
Date of Acceptance:	15 February 2026
Last Modified:	03 Mar 2026 11:00
URI:	https://orca.cardiff.ac.uk/id/eprint/185399

Actions (repository staff only)

Edit Item