### Abstract

Original language | English |
---|---|

Title of host publication | Integral Methods in Science and Engineering, Volume 1 |

Subtitle of host publication | Analytic Methods |

Editors | C Constanda, M E Perez |

Place of Publication | Boston |

Publisher | Birkhauser |

Pages | 53-63 |

Number of pages | 11 |

Volume | 1 |

ISBN (Electronic) | 9780817648992 |

ISBN (Print) | 9780817648985 |

DOIs | |

Publication status | Published - 2010 |

Event | 10th International Conference on Integral Methods in Science and Engineering, IMSE 2008 - Santander, Spain Duration: 7 Jul 2010 → 10 Jul 2010 |

### Conference

Conference | 10th International Conference on Integral Methods in Science and Engineering, IMSE 2008 |
---|---|

Country | Spain |

City | Santander |

Period | 7/07/10 → 10/07/10 |

### Fingerprint

### Cite this

*Integral Methods in Science and Engineering, Volume 1: Analytic Methods*(Vol. 1, pp. 53-63). Boston: Birkhauser. https://doi.org/10.1007/978-0-8176-4899-2-6

**The bottom of the spectrum in a double-contrast periodic model.** / Babych, N.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Integral Methods in Science and Engineering, Volume 1: Analytic Methods.*vol. 1, Birkhauser, Boston, pp. 53-63, 10th International Conference on Integral Methods in Science and Engineering, IMSE 2008, Santander, Spain, 7/07/10. https://doi.org/10.1007/978-0-8176-4899-2-6

}

TY - GEN

T1 - The bottom of the spectrum in a double-contrast periodic model

AU - Babych, N

PY - 2010

Y1 - 2010

N2 - A periodic spectral problem in a bounded domain with double inhomogeneities in mass density and stiffness coefficients is considered. A previous study [BKS08] has explored the problem by the method of asymptotic expansions with justification of errors showing that all eigenelements of the homogenized problem really approximate some of the perturbed eigenelements. Within this chapter additional results, partly announced in [BKS08], are obtained on the eigenfunction convergence at the bottom of the spectrum. It is shown that the eigenfunctions, which correspond to the eigenvalues at the bottom of the spectrum, could converge either to zero or to the eigenfunctions of the homogenized problem. The result was obtained by the method of two-scale convergence [Al92, Zh00].

AB - A periodic spectral problem in a bounded domain with double inhomogeneities in mass density and stiffness coefficients is considered. A previous study [BKS08] has explored the problem by the method of asymptotic expansions with justification of errors showing that all eigenelements of the homogenized problem really approximate some of the perturbed eigenelements. Within this chapter additional results, partly announced in [BKS08], are obtained on the eigenfunction convergence at the bottom of the spectrum. It is shown that the eigenfunctions, which correspond to the eigenvalues at the bottom of the spectrum, could converge either to zero or to the eigenfunctions of the homogenized problem. The result was obtained by the method of two-scale convergence [Al92, Zh00].

UR - http://link.springer.com/chapter/10.1007/978-0-8176-4899-2_6

U2 - 10.1007/978-0-8176-4899-2-6

DO - 10.1007/978-0-8176-4899-2-6

M3 - Conference contribution

SN - 9780817648985

VL - 1

SP - 53

EP - 63

BT - Integral Methods in Science and Engineering, Volume 1

A2 - Constanda, C

A2 - Perez, M E

PB - Birkhauser

CY - Boston

ER -