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Spectrum of a diffusion operator with coefficient changing sign over a small inclusion. / Chesnel, L.; Claeys, X.; Nazarov, S.A.

в: Zeitschrift für angewandte Mathematik und Physik, № 5, 2015, стр. 2173-2196.

Результаты исследований: Научные публикации в периодических изданиях › статья

Harvard

Chesnel, L, Claeys, X & Nazarov, SA 2015, 'Spectrum of a diffusion operator with coefficient changing sign over a small inclusion', Zeitschrift für angewandte Mathematik und Physik, № 5, стр. 2173-2196. https://doi.org/10.1007/s00033-015-0559-1

APA

Chesnel, L., Claeys, X., & Nazarov, S. A. (2015). Spectrum of a diffusion operator with coefficient changing sign over a small inclusion. Zeitschrift für angewandte Mathematik und Physik, (5), 2173-2196. https://doi.org/10.1007/s00033-015-0559-1

Vancouver

Chesnel L, Claeys X, Nazarov SA. Spectrum of a diffusion operator with coefficient changing sign over a small inclusion. Zeitschrift für angewandte Mathematik und Physik. 2015;(5):2173-2196. https://doi.org/10.1007/s00033-015-0559-1

Author

Chesnel, L. ; Claeys, X. ; Nazarov, S.A. / Spectrum of a diffusion operator with coefficient changing sign over a small inclusion. в: Zeitschrift für angewandte Mathematik und Physik. 2015 ; № 5. стр. 2173-2196.

BibTeX

@article{76177fc536ed489b8c8bdb5228687f1c,
title = "Spectrum of a diffusion operator with coefficient changing sign over a small inclusion",
abstract = "{\textcopyright} 2015, Springer Basel.We study a spectral problem (Pδ) for a diffusion-like equation in a 3D domain Ω. The main originality lies in the presence of a parameter σδ, whose sign changes on Ω, in the principal part of the operator we consider. More precisely, σδ is positive on Ω except in a small inclusion of size δ>0. Because of the sign change of σδ, for all δ>0, the spectrum of (Pδ) consists of two sequences converging to ±∞. However, at the limit δ=0, the small inclusion vanishes so that there should only remain positive spectrum for (Pδ). What happens to the negative spectrum? In this paper, we prove that the positive spectrum of (Pδ) tends to the spectrum of the problem without the small inclusion. On the other hand, we establish that each negative eigenvalue of (Pδ) behaves like δ-2μ for some constant μ",
author = "L. Chesnel and X. Claeys and S.A. Nazarov",
year = "2015",
doi = "10.1007/s00033-015-0559-1",
language = "English",
pages = "2173--2196",
journal = "Zeitschrift fur Angewandte Mathematik und Physik",
issn = "0044-2275",
publisher = "Birkh{\"a}user Verlag AG",
number = "5",

}

RIS

TY - JOUR

T1 - Spectrum of a diffusion operator with coefficient changing sign over a small inclusion

AU - Chesnel, L.

AU - Claeys, X.

AU - Nazarov, S.A.

PY - 2015

Y1 - 2015

N2 - © 2015, Springer Basel.We study a spectral problem (Pδ) for a diffusion-like equation in a 3D domain Ω. The main originality lies in the presence of a parameter σδ, whose sign changes on Ω, in the principal part of the operator we consider. More precisely, σδ is positive on Ω except in a small inclusion of size δ>0. Because of the sign change of σδ, for all δ>0, the spectrum of (Pδ) consists of two sequences converging to ±∞. However, at the limit δ=0, the small inclusion vanishes so that there should only remain positive spectrum for (Pδ). What happens to the negative spectrum? In this paper, we prove that the positive spectrum of (Pδ) tends to the spectrum of the problem without the small inclusion. On the other hand, we establish that each negative eigenvalue of (Pδ) behaves like δ-2μ for some constant μ

AB - © 2015, Springer Basel.We study a spectral problem (Pδ) for a diffusion-like equation in a 3D domain Ω. The main originality lies in the presence of a parameter σδ, whose sign changes on Ω, in the principal part of the operator we consider. More precisely, σδ is positive on Ω except in a small inclusion of size δ>0. Because of the sign change of σδ, for all δ>0, the spectrum of (Pδ) consists of two sequences converging to ±∞. However, at the limit δ=0, the small inclusion vanishes so that there should only remain positive spectrum for (Pδ). What happens to the negative spectrum? In this paper, we prove that the positive spectrum of (Pδ) tends to the spectrum of the problem without the small inclusion. On the other hand, we establish that each negative eigenvalue of (Pδ) behaves like δ-2μ for some constant μ

U2 - 10.1007/s00033-015-0559-1

DO - 10.1007/s00033-015-0559-1

M3 - Article

SP - 2173

EP - 2196

JO - Zeitschrift fur Angewandte Mathematik und Physik

JF - Zeitschrift fur Angewandte Mathematik und Physik

SN - 0044-2275

IS - 5

ER -

ID: 4011607