Homogenization of Evolution Problems in a Fiber Reinforced Structure
Michel Bellieud · Journal of convex analysis · 2004
We study the homogenization of parabolic or hyperbolic equations like \rho_\epsilon(x){\partial^n u_\epsilon \over \partial t^n}- div(a_\epsilon(x) abla u_\epsilon) =f ρ ϵ ( x ) ∂ n u ϵ ∂ t n − d i v ( a ϵ ( x ) ∇ u ϵ ) = f on \Omega\times (0, T) Ω × ( 0 , T ) plus boundary conditions, n \in \{1,2\} n ∈ { 1 , 2 } , where the coefficients a_\epsilon a ϵ and \rho_\epsilon ρ ϵ takes values of very different order on an \epsilon ϵ -periodic subset T_\epsilon \subset \Omega T ϵ ⊂ Ω (fibered structure) and elsewhere. We find a non local effective equation deduced from a homogenized system of several equations.