Abstract

We study the homogenization of parabolic or hyperbolic equations like ρϵ(x)∂nuϵ∂tn−div(aϵ(x)∇uϵ)=f\rho_\epsilon(x){\partial^n u_\epsilon \over \partial t^n}- div(a_\epsilon(x) \nabla u_\epsilon) =f on Ω×(0,T)\Omega\times (0, T) plus boundary conditions, n∈{1,2}n \in \{1,2\}, where the coefficients aϵa_\epsilon and ρϵ\rho_\epsilon takes values of very different order on an ϵ\epsilon-periodic subset Tϵ⊂ΩT_\epsilon \subset \Omega (fibered structure) and elsewhere. We find a non local effective equation deduced from a homogenized system of several equations.

Author information

Contact details are reproduced from the original publication and may be historical.

Michel Bellieud

Dep. de Mathématiques, Université de Perpignan, 52 av. de Villeneuve, 66100 Perpignan, France

bellieud@univ-tln.fr

Keywords

  • homogenization
  • fiber structures
  • two-scale convergence
  • Γ-convergence

Mathematics Subject Classification

35B40, 35J55, 74B05, 74K10, 74Q15

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Suggested citation

M. Bellieud. “Homogenization of Evolution Problems in a Fiber Reinforced Structure.” Journal of Convex Analysis 11 (2004), No. 2, 363–385. https://doi.org/10.68381/jca11022

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Published by Heldermann Verlag, 2004. Rights now held by Banach Press LLC.