Body resonances for classical waves

2024/06/24 by Mantile, Andrea, Posilicano, Andrea · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2406.17130

Abstract

We provide a detailed study of the spectral properties of the linear operator H(ε)=-(ε²χ_Ω_ε+χ_Ω^c_ε)Δ modeling, through the wave equation (∂_tt+H(ε))u=0, the dynamics of acoustic waves in the presence of a small inhomogeneity of size ε having high contrast ε^-2. In particular, we give precise results on the localization of the resonances of H(ε) and their first-order ε-expansions; the latter are explicitly expressed in terms of the eigenvalues and eigenvectors of the Newton potential operator of the set Ω whose rescaling of size ε defines Ω_ε.

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