Research output: Contribution to journal › Article › peer-review
Localization effects for Dirichlet problems in domains surrounded by thin stiff and heavy bands. / Gómez, Delfina; Nazarov, Sergei A.; Pérez-Martínez, Maria Eugenia.
In: Journal of Differential Equations, Vol. 270, 01.01.2021, p. 1160-1195.Research output: Contribution to journal › Article › peer-review
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TY - JOUR
T1 - Localization effects for Dirichlet problems in domains surrounded by thin stiff and heavy bands
AU - Gómez, Delfina
AU - Nazarov, Sergei A.
AU - Pérez-Martínez, Maria Eugenia
N1 - Funding Information: This work has partially been supported by the Spanish MICINN grant PGC2018-098178-B-I00 , the Russian Foundation for Basic Research 18-01-00325 and the Convenium Banco Santander - Universidad de Cantabria 2018. Publisher Copyright: © 2020 Elsevier Inc. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.
PY - 2021/1/1
Y1 - 2021/1/1
N2 - We consider a Dirichlet spectral problem for a second order differential operator, with piecewise constant coefficients, in a domain Omega(epsilon) in the plane R-2. Here Omega(epsilon) is Omega boolean OR omega(epsilon) boolean OR Gamma, where Omega is a fixed bounded domain with boundary Gamma, omega(epsilon) is a curvilinear band of width O(epsilon), and Gamma = (Omega) over bar boolean AND (omega) over bar (epsilon). The density and stiffness constants are of order epsilon(-m-t) and epsilon(-t) respectively in this band, while they are of order 1 in Omega; t >= 1, m > 2, and s is a small positive parameter. We address the asymptotic behavior, as epsilon -> 0, for the eigenvalues and the corresponding eigenfunctions. In particular, we show certain localization effects for eigenfunctions associated with low frequencies. This is deeply involved with the extrema of the curvature of Gamma. (C) 2020 Elsevier Inc. All rights reserved.
AB - We consider a Dirichlet spectral problem for a second order differential operator, with piecewise constant coefficients, in a domain Omega(epsilon) in the plane R-2. Here Omega(epsilon) is Omega boolean OR omega(epsilon) boolean OR Gamma, where Omega is a fixed bounded domain with boundary Gamma, omega(epsilon) is a curvilinear band of width O(epsilon), and Gamma = (Omega) over bar boolean AND (omega) over bar (epsilon). The density and stiffness constants are of order epsilon(-m-t) and epsilon(-t) respectively in this band, while they are of order 1 in Omega; t >= 1, m > 2, and s is a small positive parameter. We address the asymptotic behavior, as epsilon -> 0, for the eigenvalues and the corresponding eigenfunctions. In particular, we show certain localization effects for eigenfunctions associated with low frequencies. This is deeply involved with the extrema of the curvature of Gamma. (C) 2020 Elsevier Inc. All rights reserved.
KW - Asymptotic analysis
KW - Localized eigenfunctions
KW - Spectral analysis
KW - Stiff problem
KW - LAPLACIAN
KW - EIGENVALUES
KW - ASYMPTOTIC EXPANSIONS
KW - SYSTEMS
KW - EIGENFUNCTIONS
KW - SPECTRUM
UR - http://www.scopus.com/inward/record.url?scp=85091247536&partnerID=8YFLogxK
UR - https://www.mendeley.com/catalogue/c4403626-40a9-3ee1-8b88-0d984c40d72e/
U2 - 10.1016/j.jde.2020.09.011
DO - 10.1016/j.jde.2020.09.011
M3 - Article
AN - SCOPUS:85091247536
VL - 270
SP - 1160
EP - 1195
JO - Journal of Differential Equations
JF - Journal of Differential Equations
SN - 0022-0396
ER -
ID: 71561827