Quantitative homogenization of attractors of non-Newtonian filtration equations
type: Item
instance of: scholarly article
title: Quantitative homogenization of attractors of non-Newtonian filtration equations
zbMATH Open document ID: 1333.37115
DOI: 10.1155/2010/173408
author: Emil Novruzov
published in: Mathematical Problems in Engineering
publication date: 2010-06-29T00:00:00Z
review text: Summary: For a rapidly spatially oscillating nonlinearity \(g\) we compare solutions \(u^\varepsilon\) of a non-Newtonian filtration equation \[ \partial_t\beta(u^\varepsilon)-D(| Du^\varepsilon|^{p-2}Du^\varepsilon+\varphi(u^\varepsilon)Du^\varepsilon)+ g(x, x/\varepsilon, u^\varepsilon) = f(x, x/\varepsilon) \] with solutions \(u^0\) of the homogenized, spatially averaged equation \[ \partial_t\beta(u^0) - D(| Du^0|^{p-2}Du^0)+\varphi(u^0)Du^0) + g^0(x, u^0)= f^0(x). \] Based on an \(\varepsilon\)-independent a priori estimate, we prove that \[ \|\beta(u^\varepsilon)-\beta(u^0)\|_{L^1(\Omega)} \leq C\varepsilon e^{\rho t} \] uniformly for all \(t\geq 0\). Besides, we give an explicit estimate for the distance between the nonhomogenized \(A^\varepsilon\) and the homogenized \(A^0\) attractors in terms of the parameter \(\varepsilon\); precisely, we show fractional-order semicontinuity of the global attractors for \(\varepsilon\searrow 0: \text{dist}_{L^1(\Omega)}(A^\varepsilon,A^0)\leq C\varepsilon^\gamma\).
Mathematics Subject Classification ID: 37L30
Mathematics Subject Classification ID: 35B27
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 37N10
Mathematics Subject Classification ID: 76A05
Mathematics Subject Classification ID: 76S05
zbMATH DE Number: 5728469
Wikidata QID: Q58652949
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2010/173408
OpenAlex ID: W2054142986
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description: scientific article; zbMATH DE number 5728469