Homogenized Model of Diffusion in Porous Media with Nonlinear Absorption on the Boundary

Homogenized Model of Non-Stationary Diffusion in Porous Media with the Drift

“…First we obtain the estimates for the time derivative of the solution and the drift term to transform the parabolic problem to the elliptic one. Then, using Theorem 1 from [12], we obtain the homogenized model of the initial problem.…”

“…For periodically perforated domains, the equation with the linear Robin condition was studied in [7][8][9] and for the strongly connected domains with linear absorption in [4]. The problem of a stationary diffusion without drift is studied in [12], and the result is used in this paper.…”

Integral Conditions for Convergence of Solutions of Non-Linear Robin's Problem in Strongly Perforated Domain

“…We briefly outline the scheme of the proof. It is similar to the scheme developed in [9], but it should be taken into account that the conditions of the uniform convergence does not hold in the entire region Ω.…”

“…However, the domains Ω ε of an arbitrary form (including the connected perforating sets F ε ) are more natural from the physical point view. Earlier, in [9] we considered problem (1) in the domains Ω ε of an arbitrary form satisfying only one important condition: the condition of strong connectedness (this condition was introduced in [12]). It was shown that the solution u ε (x) of problem (1) converges as ε → 0 in the L 2 (Ω ε ) metric to the solution u(x) of the homogenized problem in the domain Ω:…”

“…In [9], it is assumed that uniformly with respect to x ∈ Ω there exists a density of mesoscopic characteristic:…”