Homogenization of discrete thin structures

نویسندگان

چکیده

We consider graphs parameterized on a portion X⊂Zd×{1,…,M}k of cylindrical subset the lattice Zd×Zk, and perform discrete-to-continuum dimension-reduction process for energies defined X quadratic type. Our only assumptions are that be connected as graph periodic in first d-directions. show that, upon scaling domain by small parameter ɛ, scaled converge to d-dimensional limit energy. The main technical points dimension-reducing coarse-graining discrete version p-connectedness approach Zhikov.

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ژورنال

عنوان ژورنال: Nonlinear Analysis-theory Methods & Applications

سال: 2023

ISSN: ['1873-5215', '0362-546X']

DOI: https://doi.org/10.1016/j.na.2022.112951