Homogenization of an Eigenvalue Problem with a Robin Condition in Perforated Domains

Patrizia Donato () and María-Eugenia Pérez-Martínez ()
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Patrizia Donato: Université de Rouen Normandie
María-Eugenia Pérez-Martínez: Universidad de Cantabria

Chapter Chapter 8 in Integral Methods in Science and Engineering, 2026, pp 121-135 from Springer

Abstract: Abstract In this paper we address the asymptotic behavior of a spectral problem associated with a diffusion model in nonhomogeneous perforate periodic media of ℝ N $$\mathbb {R}^N$$ with N ≥ 2 $$N\geq 2$$ . The size of the perforations, the holes, and the period are of the same order of magnitude O ( ε ) $$O(\varepsilon )$$ while a Robin boundary condition is imposed on the boundary of the holes containing the parameter ε $$ \varepsilon $$ multiplied by a periodic function ρ ε $$\rho _\varepsilon $$ . The homogenized problem is obtained via the unfolding method, while the convergence of the spectrum with conservation of the multiplicity requires techniques from spectral perturbation theory.

Date: 2026
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DOI: 10.1007/978-3-032-04458-7_8

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