Σ-convergence of nonlinear monotone operators in perforated domains with holes of small size
- 81 Downloads
This paper is devoted to the homogenization beyond the periodic setting, of nonlinear monotone operators in a domain in ℝ N with isolated holes of size ɛ2 (ɛ > 0 a small parameter). The order of the size of the holes is twice that of the oscillations of the coefficients of the operator, so that the problem under consideration is a reiterated homogenization problem in perforated domains. The usual periodic perforation of the domain and the classical periodicity hypothesis on the coefficients of the operator are here replaced by an abstract assumption covering a great variety of behaviors such as the periodicity, the almost periodicity and many more besides. We illustrate this abstract setting by working out a few concrete homogenization problems. Our main tool is the recent theory of homogenization structures.
Keywordsperforated domains homogenization reiterated
MSC 200035B40 46J10
Unable to display preview. Download preview PDF.
- N. Bourbaki: Éléments de mathématique. Intégration, Chap. 1–4. Hermann, Paris, 1966. (In French.)Google Scholar
- N. Bourbaki: Éléments de matématique. Topologie générale, Chap. 1–4. Hermann, Paris, 1971. (In French.)Google Scholar
- D. Cioranescu, F. Murat: Un terme étrange venu d’ailleurs. Nonlin. partial differential equations and their applications, Coll. de France Semin., Vol. II, Vol. III. Res. Notes Math. (1982), 98–138, 154–178. (In French.)Google Scholar
- G. Nguetseng: Almost periodic homogenization Asymptotic analysis of a second order elliptic equation. Preprint.Google Scholar
- G. Nguetseng, H. Nnang: Homogenization of nonlinear monotone operators beyond the periodic setting. Electron. J. Differ. Equ. 2003 (2003).Google Scholar
- G. Nguetseng, J. L. Woukeng: Deterministic homogenization of parabolic monotone operators with time dependent coefficients. Electron. J. Differ. Equ. 2004 (2004).Google Scholar