Stochastic homogenization of Λ-convex gradient flows
- Heida, Martin
- Neukamm, Stefan
- Varga, Mario
2010 Mathematics Subject Classification
- 49J40 74Q10 35K57
- Stochastic homogenization, stochastic unfolding, two-scale convergence, gradient system
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.