Repository: Freie Universität Berlin, Math Department

Stochastic homogenization of Λ-convex gradient flows

Heida, M. and Neukamm, S. and Varga, M. (2019) Stochastic homogenization of Λ-convex gradient flows. SFB 1114 Preprint in arXiv:1905.02562 . pp. 1-28. (Unpublished)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 Λ-convex energy functional featuring random and rapidly oscillating coefficients. Specific examples included in the result are Allen-Cahn type equations and evolutionary equations driven by the p-Laplace operator with p∈(1,∞). The homogenization procedure we apply is based on a stochastic two-scale convergence approach. In particular, we define a stochastic unfolding operator which can be considered as a random counterpart of the well-established 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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