Repository: Freie Universität Berlin, Math Department


Heida, Martin and Neukamm, Stefan and Varga, Mario (2021) STOCHASTIC HOMOGENIZATION OF L-CONVEX GRADIENT FLOWS. Discrete and Continuous Dynamical Systems - S, 14 (1). pp. 1-27.

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Official URL: http://doi:10.3934/dcdss.2020328


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.

Item Type:Article
Subjects:Mathematical and Computer Sciences > Mathematics > Applied Mathematics
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics
ID Code:2653
Deposited By: Monika Drueck
Deposited On:17 Jan 2022 13:50
Last Modified:22 Feb 2022 17:37

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