Homogenization of nonlocal spectral problems

2024/01/29 by Andrey Piatnitski, Piatnitski, Andrey, Volodymyr Rybalko +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2401.16576

openalex publication_date 2024/01/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study asymptotic behavior of the bottom point of the spectrum of convolution type operators in environments with locally periodic microstructure. We show that its limit is described by an additive eigenvalue problem for Hamilton-Jacobi equation. In the periodic case we establish a more accurate two-term asymptotic formula.

Related

• Periodic homogenization of non-local operators with a convolution type\n kernel
• Homogenisation and spectral convergence of high-contrast convolution type operators
• Multiscale homogenization of non-local energies of convolution-type
• Periodic homogenization of convolution type operators with heavy tails
• Homogenization of the spectral equation in one-dimension