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Article Dans Une Revue Indiana University Mathematics Journal Année : 2003

Homogenization and localization with an interface

Résumé

We consider the homogenization of a spectral problem for a diffusion equation posed in a singularly perturbed periodic medium. Denoting by ε the period, the diffusion coefficients are scaled as ε 2. The domain is composed of two periodic medium separated by a planar interface, aligned with the periods. Three different situations arise when ε goes to zero. First, there is a global homogenized problem as if there were no interface. Second, the limit is made of two homogenized problems with a Dirichlet boundary condition on the interface. Third, there is an exponential localization near the interface of the first eigenfunc-tion.
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Dates et versions

hal-02083811 , version 1 (04-08-2020)

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Grégoire Allaire, Yves Capdeboscq, Andrey Piatnitski. Homogenization and localization with an interface. Indiana University Mathematics Journal, 2003, 52 (6), pp.1413--1446. ⟨10.1512/iumj.2003.52.2352⟩. ⟨hal-02083811⟩
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