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Original Articles

Applications of periodic unfolding on manifolds

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Pages 55-68 | Received 20 Jan 2017, Accepted 09 Jun 2017, Published online: 19 Jun 2017
 

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.

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Notes

No potential conflict of interest was reported by the author.

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