Homogenization of periodic systems with large potentials

Allaire, Grégoire ; Capdeboscq, Yves ; Piatnitski, Andrey ; Siess, Vincent ; Vanninathan, M. (2004) Homogenization of periodic systems with large potentials Archive for Rational Mechanics and Analysis, 174 (2). pp. 179-220. ISSN 0003-9527

PDF - Author Version

Official URL: http://www.springerlink.com/content/6eupty28bjha5w...

Related URL: http://dx.doi.org/10.1007/s00205-004-0332-7


We consider the homogenization of a system of second-order equations with a large potential in a periodic medium. Denoting by ε the period, the potential is scaled as ε−2. Under a generic assumption on the spectral properties of the associated cell problem, we prove that the solution can be approximately factorized as the product of a fast oscillating cell eigenfunction and of a slowly varying solution of a scalar second-order equation. This result applies to various types of equations such as parabolic, hyperbolic or eigenvalue problems, as well as fourth-order plate equation. We also prove that, for well-prepared initial data concentrating at the bottom of a Bloch band, the resulting homogenized tensor depends on the chosen Bloch band. Our method is based on a combination of classical homogenization techniques (two-scale convergence and suitable oscillating test functions) and of Bloch waves decomposition.

Item Type:Article
Source:Copyright of this article belongs to Springer.
ID Code:55307
Deposited On:18 Aug 2011 07:05
Last Modified:18 May 2016 07:37

Repository Staff Only: item control page