Displaying similar documents to “Homogenization of evolution problems for a composite medium with very small and heavy inclusions”

The method of Rothe and two-scale convergence in nonlinear problems

Jiří Vala (2003)

Applications of Mathematics

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Modelling of macroscopic behaviour of materials, consisting of several layers or components, cannot avoid their microstructural properties. This article demonstrates how the method of Rothe, described in the book of K. Rektorys The Method of Discretization in Time, together with the two-scale homogenization technique can be applied to the existence and convergence analysis of some strongly nonlinear time-dependent problems of this type.

Multiscale convergence and reiterated homogenization of parabolic problems

Anders Holmbom, Nils Svanstedt, Niklas Wellander (2005)

Applications of Mathematics

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Reiterated homogenization is studied for divergence structure parabolic problems of the form ∂ u ε / ∂ t - div a x , x / ε , x / ε 2 , t , t / ε k ∇ u ε = f . It is shown that under standard assumptions on the function a ( x , y 1 , y 2 , t , τ ) the sequence { u ϵ } of solutions converges weakly in L 2 ( 0 , T ; H 0 1 ( Ω ) ) to the solution u of the homogenized problem ∂ u / ∂ t - div ( b ( x , t ) ∇ u ) = f .

A generalized strange term in Signorini’s type problems

Carlos Conca, François Murat, Claudia Timofte (2003)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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The limit behavior of the solutions of Signorini’s type-like problems in periodically perforated domains with period ε is studied. The main feature of this limit behaviour is the existence of a critical size of the perforations that separates different emerging phenomena as ε → 0 . In the critical case, it is shown that Signorini’s problem converges to a problem associated to a new operator which is the sum of a standard homogenized operator and an extra zero order term (“strange term”) coming...