✦ LIBER ✦
Homogenization of eigenvalue problem for Laplace–Beltrami operator on Riemannian manifold with complicated ‘bubble-like’ microstructure
✍ Scribed by Andrii Khrabustovskyi
- Publisher
- John Wiley and Sons
- Year
- 2009
- Tongue
- English
- Weight
- 151 KB
- Volume
- 32
- Category
- Article
- ISSN
- 0170-4214
- DOI
- 10.1002/mma.1128
No coin nor oath required. For personal study only.
✦ Synopsis
Abstract
We study the asymptotic behavior of the eigenvalues and the eigenfunctions of the Laplace–Beltrami operator on a Riemannian manifold M^ε^ depending on a small parameter ε>0 and whose structure becomes complicated as ε→0. Under a few assumptions on scales of M^ε^ we obtain the homogenized eigenvalue problem. In addition we study the behavior of the heat equation on M^ε^ and investigate the large time behavior of the homogenized equation. Copyright © 2009 John Wiley & Sons, Ltd.