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Asymptotics for models of non‐stationary diffusion in domains with a surface distribution of obstacles
Author(s) -
Gómez Delfina,
Lobo Miguel,
PérezMartínez MaríaEugenia
Publication year - 2018
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.5323
Subject(s) - mathematics , nonlinear system , mathematical analysis , monotone polygon , advection , partial differential equation , domain (mathematical analysis) , boundary (topology) , diffusion , compressibility , function (biology) , distribution function , reynolds number , mechanics , geometry , physics , thermodynamics , quantum mechanics , evolutionary biology , biology , turbulence
We consider a time‐dependent model for the diffusion of a substance through an incompressible fluid in a perforated domain Ω ϵ , Ω ϵ ⊂ Ω ⊂ R n with n = 3,4. The fluid flows in a domain containing a periodical set of “obstacles” (Ω\Ω ϵ ) placed along an inner ( n − 1)‐dimensional manifold Σ ⊂ Ω . The size of the obstacles is much smaller than the size of the characteristic period ϵ . An advection term appears in the partial differential equation linking the fluid velocity with the concentration, while we assume a nonlinear adsorption law on the boundary of the obstacles. This law involves a monotone nonlinear function σ of the concentration and a large adsorption parameter. The “critical adsorption parameter” depends on the size of the obstacles , and, for different sizes, we derive the time‐dependent homogenized models. These models contain a “strange term” in the transmission conditions on Σ, which is a nonlinear function and inherits the properties of σ . The case in which the fluid velocity and the concentration do not interact is also considered for n ≥ 3.