Nonstationary flow of a viscous fluid through a porous elastic medium: Asymptotic analysis and two-scale convergence (Q1572737)

The authors investigate the nonstationary Stokes flow through a linear elastic porous medium with a periodic structure. The homogenized flow (when the periodicity tends to zero) is identified by the use of two-scale convergence method [\textit{G. Allaire}, SIAM J. Math Anal. 23, No. 6, 1482-1518 (1992; Zbl 0770.35005); \textit{G. Nguetseng}, SIAM J. Math. Anal. 20, No. 3, (1989; Zbl 0688.35007)]. The obtained results extend those due to \textit{G. Allaire} [in \textit{C. Bandle} (ed.); \textit{J. Bemelmans} (ed.); \textit{M. Chipot} (ed.); \textit{M. Grüter} (ed.); \textit{J. Saint Jean Paulin} (ed.) Progress in partial differential equations: calculus of variations, applications. 1st European conference on elliptic and parabolic problems, Pont-á-Mousson, France, June 1991. Pitman Research Notes in Mathematics Series 267. Harlow, Essex: Longman Scientific \& Technical New York: Wiley (1993; Zbl 0780.00014)] and \textit{A. Mikelić} [Glas. Mat., III. Ser. 29, No. 1, 57-77 (1994; Zbl 0815.35086)].