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arXiv · 1410.3376

Variational Approach to Homogenization of Doubly-Nonlinear Flow in a Periodic Structure

A. K. Nandakumaran·Augusto Visintin
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Abstract

This work deals with the homogenization of an initial- and boundary-value problem for the doubly-nonlinear system $$ D_t w -\nabla\cdot \vec z = \nabla\cdot \vec h(x,t,x/\varepsilon), \qquad w\in α(u,x/\varepsilon), \qquad \vec z\in \vecγ(\nabla u,x/\varepsilon). $$ Here $\varepsilon$ is a positive parameter, and the prescribed mappings $α$ and $\vecγ$ are maximal monotone with respect to the first variable and periodic with respect to the second one. The two inclusions are here formulated as null-minimization principles, via the theory of Fitzpatrick [MR 1009594]. As $\varepsilon\to 0$, a two-scale formulation is derived via Nguetseng's notion of two-scale convergence, and a (single-scale) homogenized problem is then retrieved.

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A. K. Nandakumaran, Augusto Visintin. 2014-10-13. Variational Approach to Homogenization of Doubly-Nonlinear Flow in a Periodic Structure. https://arxiv.org/abs/1410.3376

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