Multiscale homogenization with bounded ratios and anomalous slow diffusion
Article first published online: 29 OCT 2002
Copyright © 2003 Wiley Periodicals, Inc.
Communications on Pure and Applied Mathematics
Volume 56, Issue 1, pages 80–113, January 2003
How to Cite
Ben Arous, G. and Owhadi, H. (2003), Multiscale homogenization with bounded ratios and anomalous slow diffusion. Comm. Pure Appl. Math., 56: 80–113. doi: 10.1002/cpa.10053
- Issue published online: 29 OCT 2002
- Article first published online: 29 OCT 2002
- Manuscript Received: DEC 2001
We show that the effective diffusivity matrix D(Vn) for the heat operator ∂t − (Δ/2 − ∇Vn∇) in a periodic potential Vn = ΣUk(x/Rk) obtained as a superposition of Hölder-continuous periodic potentials Uk (of period d := ℝd/ℤd, d ∈ ℕ*, Uk(0) = 0) decays exponentially fast with the number of scales when the scale ratios Rk+1/Rk are bounded above and below. From this we deduce the anomalous slow behavior for a Brownian motion in a potential obtained as a superposition of an infinite number of scales, dyt = dωt − ∇V∞(yt)dt. © 2002 Wiley Periodicals, Inc.