Homogenization in thin cylinders

This Note announces our works [10] and [11] in which we consider simultaneo usly the homogenization and the reduction of dimension 3d-1d in the thermal conduction equation as well as in the linearized system of elasticity. We study the asymptotic analysis, as epsilon tends to zero, of these two probl ems posed on a cylinder Omega (epsilon) = epsilonw x (0,L), made from a com posite material having a periodic structure with the period epsilon along t he cylinder axis and with the period epsilon (2) over the section w of the cylinder. We prove that the limit problem is a coupled system where appear two entities: the first one is related on the reduction of the dimension 3d -1d, and the second one is related on the homogenization process. We also g ive a corrector result. (C) 2001 Academics des sciences/Editions scientifiq ues et medicales Elsevier SAS.