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Article Dans Une Revue Annali di Matematica Pura ed Applicata Année : 2002

Homogenization and localization for a 1-D eigenvalue problem in a periodic medium with an interface

Yves Capdeboscq

Résumé

In one space dimension we address the homogenization of the spectral problem for a singularly perturbed diffusion equation in a periodic medium. Denoting by the period, the diffusion coefficient is scaled as 2. The domain is made of two purely periodic media separated by an interface. Depending on the connection between the two cell spectral equations, three different situations arise when goes to zero. First, there is a global homogenized problem as in the case without an 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 eigenfunction.
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Dates et versions

hal-02083808 , version 1 (04-08-2020)

Identifiants

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Grégoire Allaire, Yves Capdeboscq. Homogenization and localization for a 1-D eigenvalue problem in a periodic medium with an interface. Annali di Matematica Pura ed Applicata, 2002, 181 (3), pp.247--282. ⟨10.1007/s102310100040⟩. ⟨hal-02083808⟩
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