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Long time approximations for solutions of wave equations associated with the Steklov spectral homogenization problems

Abstract: The interest in the use of quasimodes, or almost frequencies and almost eigenfunctions, to describe asymptotics for low-frequency and high-frequency vibrations in certain singularly perturbed spectral problems, which depend on a small parameter ?, has been recently highlighted in many papers. In this paper we deal with the low frequencies for a Steklov-type eigenvalue homogenization problem: we consider harmonic functions in a bounded domain of ?2, and strongly alternating boundary conditions of the Dirichlet and Steklov type on a part of the boundary. The spectral parameter appears in the boundary condition on small segments T? of size O(?) periodically distributed along the boundary; ? also measures the periodicity of the structure. We consider associated second-order evolution problems on spaces of traces that depend on ?, and we provide estimates for the time t in which standing waves, constructed from quasimodes, approach their solutions u?(t) as ??0.

 Autoría: Lobo M., Pérez M.,

 Fuente: Mathematical Methods in the Applied Sciences 2010,33(11),1356-1371

Editorial: John Wiley & Sons

 Fecha de publicación: 30/07/2010

Nº de páginas: 16

Tipo de publicación: Artículo de Revista

 DOI: 10.1002/mma.1256

ISSN: 0170-4214,1099-1476

Proyecto español: MTM2005-07720

Url de la publicación: https://onlinelibrary.wiley.com/doi/10.1002/mma.1256