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We study the problem of correctors in the framework of the homogenization of linear parabolic equations posed in a heterogeneous medium $\mathrm{\Omega }$ made of two materials. The first one is located in a set $F_{ϵ}$ of cylindrical parallel fibers periodically distributed with a period of size $ϵ$, and the second one is located in the "matrix" $M_{ϵ}=\mathrm{\Omega }\setminus F_{ϵ}$. The ratio between the conductivity coefficients of the two materials is of order $1/{ϵ}^2$. After writing the homogenized problem, we give a corrector result and prove that the solution...

We consider the linearized elasticity system in a multidomain of ${𝐑}^3$. This multidomain is the union of a horizontal plate with fixed cross section and small thickness , and of a vertical beam with fixed height and small cross section of radius $r^{\epsilon }$. The lateral boundary of the plate and the top of the beam are assumed to be clamped. When and $r^{\epsilon }$ tend to zero simultaneously, with $r^{\epsilon }\gg {\epsilon }^2$, we identify the limit problem. This limit problem involves six junction conditions.