Stochastic homogenization of A-convex gradient flows
Publikation: Beitrag in Fachzeitschrift › Forschungsartikel › Beigetragen › Begutachtung
Beitragende
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 Lambda-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 is an element of (1, infinity). 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 (Lambda-)convex functionals.
Details
Originalsprache | Englisch |
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Seiten (von - bis) | 427-453 |
Seitenumfang | 27 |
Fachzeitschrift | Discrete and continuous dynamical systems-Series s |
Jahrgang | 14 |
Ausgabenummer | 1 |
Publikationsstatus | Veröffentlicht - Jan. 2021 |
Peer-Review-Status | Ja |
Extern publiziert | Ja |
Externe IDs
Scopus | 85098882990 |
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Schlagworte
Schlagwörter
- Stochastic homogenization, stochastic unfolding, two-scale convergence, gradient system, 2-SCALE HOMOGENIZATION, GAMMA-CONVERGENCE, RANDOM-WALKS, HILBERT, SPACES