Applications of periodic unfolding on manifolds. Issue 1 (2nd January 2018)

• Record Type: Journal Article
• Authors: Dobberschütz, Sören
• Is Part Of: Applicable analysis. Volume 97:Issue 1(2018)
• Page Start: 55
• Page End: 68
• Publication Date: 2018-01-02
• Subjects: Periodic unfolding; Riemannian manifolds -- homogenization; 35B27 -- 35J40 -- 53A99; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2017.1341974
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract: We show how the newly developed method of periodic unfolding on Riemannian manifolds can be applied to PDE problems: we consider the homogenization of an elliptic model problem. In the limit, we obtain a generalization of the well-known limit- and cell-problem. By constructing an equivalence relation of atlases, one can show the invariance of the limit problem with respect to this equivalence relation. This implies e.g. that the homogenization limit is independent of change of coordinates or scalings of the reference cell. These type of problems emerge for example when modeling surface diffusion and reactions in heterogeneous catalysts, or in processes involved in crystal formation.