Heida, M. and Neukamm, S. and Varga, M. (2019) Stochastic homogenization of Λconvex gradient flows. SFB 1114 Preprint in arXiv:1905.02562 . pp. 128. (Unpublished)

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Official URL: https://arxiv.org/abs/1905.02562
Abstract
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 Λconvex energy functional featuring random and rapidly oscillating coefficients. Specific examples included in the result are AllenCahn type equations and evolutionary equations driven by the pLaplace operator with p∈(1,∞). The homogenization procedure we apply is based on a stochastic twoscale convergence approach. In particular, we define a stochastic unfolding operator which can be considered as a random counterpart of the wellestablished notion of periodic unfolding. The stochastic unfolding procedure grants a very convenient method for homogenization problems defined in terms of (Λ)convex functionals.
Item Type:  Article 

Subjects:  Mathematical and Computer Sciences > Mathematics > Applied Mathematics 
ID Code:  2346 
Deposited By:  Silvia Hoemke 
Deposited On:  04 Jun 2019 13:32 
Last Modified:  04 Jun 2019 13:32 
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