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Linearized viscoelastic Oldroyd fluid motion in an almost periodic environment
Author(s) -
Woukeng Jean Louis
Publication year - 2014
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3026
Subject(s) - mathematics , laplace transform , homogenization (climate) , convolution (computer science) , mathematical analysis , nonlinear system , viscoelasticity , limit (mathematics) , domain (mathematical analysis) , computer science , biodiversity , ecology , physics , quantum mechanics , machine learning , artificial neural network , biology , thermodynamics
In most of the linear homogenization problems involving convolution terms so far studied, the main tool used to derive the homogenized problem is the Laplace transform. Here we propose a direct approach enabling one to tackle both linear and nonlinear homogenization problems that involve convolution sequences without using Laplace transform. To illustrate this, we investigate in this paper the asymptotic behavior of the solutions of a Stokes–Volterra problem with rapidly oscillating coefficients describing the viscoelastic fluid flow in a fixed domain. Under the almost periodicity assumption on the coefficients of the problem, we prove that the sequence of solutions of our ϵ ‐problem converges in L 2 to a solution of a rather classical Stokes system. One important fact is that the memory disappears in the limit. To achieve our goal, we use some very recent results about the sigma‐convergence of convolution sequences. Copyright © 2013 John Wiley & Sons, Ltd.