WIAS Preprint No. 2594, (2019)

Stochastic homogenization of Λ-convex gradient flows



Authors

  • Heida, Martin
  • Neukamm, Stefan
  • Varga, Mario

2010 Mathematics Subject Classification

  • 49J40 74Q10 35K57

Keywords

  • Stochastic homogenization, stochastic unfolding, two-scale convergence, gradient system

DOI

10.20347/WIAS.PREPRINT.2594

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 ∈ in (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.

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