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Abstract: This paper deals with homogenization of second order divergence formparabolic operators with locally stationary coefficients. Roughly speaking,locally stationary coefficients have two evolution scales: both an almostconstant microscopic one and a smoothly varying macroscopic one. Thehomogenization procedure aims to give a macroscopic approximation that takesinto account the microscopic heterogeneities. This paper follows -Diffusion ina locally stationary random environment- published in Probability Theory andRelated Fields and improves this latter work by considering possiblydegenerate diffusion matrices. The geometry of the homogenized equation showsthat the particle is trapped in subspace of R^d.



Author: Rémi Rhodes CEREMADE

Source: https://arxiv.org/







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