STOCHASTIC HOMOGENIZATION OF L-CONVEX GRADIENT FLOWS

Abstract

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 �-convex energy functional featuring random and rapidly oscillating coe�cients. Speci�c examples included in the result are Allen-Cahn type equations and evolutionary equations driven by the p-Laplace operator with p 2 (1;1). The homogenization procedure we apply is based on a stochastic two-scale convergence approach. In particular, we de�ne 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 de�ned in terms of (�-)convex functionals.