• Media type: E-Book; Report; Text
  • Title: Stochastic homogenization of Lambda-convex gradient flows
  • Contributor: Heida, Martin [Author]; Neukamm, Stefan [Author]; Varga, Mario [Author]
  • imprint: Weierstrass Institute for Applied Analysis and Stochastics publication server, 2019
  • Language: English
  • DOI: https://doi.org/10.20347/WIAS.PREPRINT.2594
  • Keywords: 49J40 ; 35K57 ; Stochastic homogenization -- stochastic unfolding -- two-scale convergence -- gradient system ; 74Q10 ; article
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  • Description: 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.
  • Access State: Open Access