# Two-scale homogenization of abstract linear time-dependent PDEs

@article{Neukamm2020TwoscaleHO, title={Two-scale homogenization of abstract linear time-dependent PDEs}, author={Stefan Neukamm and Mario Varga and Marcus Waurick}, journal={Asymptotic Analysis}, year={2020} }

Many time-dependent linear partial differential equations of mathematical physics and continuum mechanics can be phrased in the form of an abstract evolutionary system defined on a Hilbert space. In this paper we discuss a general framework for homogenization (periodic and stochastic) of such systems. The method combines a unified Hilbert space approach to evolutionary systems with an operator theoretic reformulation of the well-established periodic unfolding method in homogenization. Regarding…

## 2 Citations

### Stochastic homogenization of \Lambda -convex gradient flows

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In this paper we present a stochastic homogenization result for a class of Hilbert space evolutionary gradient systems driven by a quadratic dissipation potential and a $\Lambda$-convex energy…

### Stochastic two-scale convergence and Young measures

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In this paper we compare the notion of stochastic two-scale convergence in the mean (by Bourgeat, Mikelić and Wright), the notion of stochastic unfolding (recently introduced by the authors), and the…

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