A Dirichlet Spectral Problem in Domains Surrounded by Thin Stiff and Heavy Bands

Delfina Gómez (), Sergey A. Nazarov () and Maria–Eugenia Pérez-Martínez ()
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Delfina Gómez: Universidad de Cantabria
Sergey A. Nazarov: Saint-Petersburg State University
Maria–Eugenia Pérez-Martínez: Universidad de Cantabria

Chapter Chapter 6 in Computational and Analytic Methods in Science and Engineering, 2020, pp 101-126 from Springer

Abstract: Abstract We consider a Dirichlet spectral problem for a second order differential operator, with piecewise constant coefficients, in a domain Ω ε in the plane ℝ 2 $$\mathbb {R}^2$$ . Here Ω ε is Ω ∪ ω ε ∪ Γ, where Ω is a disk with boundary Γ, ω ε is an annulus of width O(ε), and Γ = Ω ¯ ∩ ω ¯ ε $$\varGamma ={\overline \varOmega }\cap {\overline \omega _\varepsilon }$$ . The density and stiffness constants are of order ε −m−t and ε −t, respectively, in this annulus, while they are of order 1 in Ω; t, m and ε are positive parameters, ε 2.

Date: 2020
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DOI: 10.1007/978-3-030-48186-5_6

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