Stochastic homogenization of Lambda-convex gradient flows
Authors
- Heida, Martin
ORCID: 0000-0002-7242-8175 - Neukamm, Stefan
ORCID: 0000-0002-8586-0661 - Varga, Mario
2010 Mathematics Subject Classification
- 49J40 74Q10 35K57
Keywords
- Stochastic homogenization, stochastic unfolding, two-scale convergence, gradient system
DOI
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.
Appeared in
- Discrete Contin. Dyn. Syst. Ser. S, 14 (2021), pp. 427--453, DOI 10.3934/dcdss.2020328 .
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