STUDY OF THE LIMIT BEHAVIOR OF A VISCOELASTIC MEDIUM WITH VERY SMALL OBSTACLES

The study the asymptotic behavior of a viscous. barotropic and compres sible fluid in a porous medium Omega(epsilon) (epsilon > 0) obtained b y removing from an open set Omega some small obstacles (T-nu(epsilon)) 1 less than or equal to nu less than or equal to n(epsilon) with a(eps ilon) much less than epsilon. We establish that the fluid behaves diff erently depending on whether the size a(epsilon) is greater than or sm aller than a critical size c(epsilon). Lf it is greater than or equal to c(epsilon) a convolution term appears in the limit problem. This co rresponds to a long memory effect. On the contrary, if the size is sma ller than c(epsilon) the fluid behaves as if there is no obstacle.