Spectral Stiff Problems in Domains with a Strongly Oscillating Boundary

D. Gómez (), S. A. Nazarov () and E. Pérez ()
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D. Gómez: Universidad de Cantabria
S. A. Nazarov: Institute for Problems in Mechanical Engineering
E. Pérez: Universidad de Cantabria

A chapter in Integral Methods in Science and Engineering, 2011, pp 159-172 from Springer

Abstract: Abstract We consider an asymptotic spectral problem for a second order differential operator, with piecewise constant coefficients, in a two-dimensional domain Ω ε which depends on a small parameter ε. Here, Ω ε is Ω ε =Ω∪ω ε ∪Γ, where Ω is a fixed open bounded domain, ω ε is a curvilinear strip of variable width O(ε), and $\Gamma={\overline{\Omega}}\cap {\overline{\omega}_{\varepsilon}}$ is the boundary of Ω. The density and stiffness constants are of order O(ε −1) and O(ε −t ), respectively, in this strip, while they are of order O(1) in the fixed domain Ω; t is a parameter such that 0≤t

Keywords: Scalar Product; Spectral Problem; Neumann Problem; Order Differential Operator; Thin Band (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1007/978-0-8176-8238-5_15

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