Displaying similar documents to “Two-scale convergence of Stekloff eigenvalue problems in perforated domains.”

Γ-convergence approach to variational problems in perforated domains with Fourier boundary conditions

Valeria Chiadò Piat, Andrey Piatnitski (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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The work focuses on the Γ-convergence problem and the convergence of minimizers for a functional defined in a periodic perforated medium and combining the bulk (volume distributed) energy and the surface energy distributed on the perforation boundary. It is assumed that the mean value of surface energy at each level set of test function is equal to zero. Under natural coercivity and -growth assumptions on the bulk energy, and the assumption that the surface energy satisfies -growth...

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.

Homogenization of evolution problems for a composite medium with very small and heavy inclusions

Michel Bellieud (2005)

ESAIM: Control, Optimisation and Calculus of Variations

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We study the homogenization of parabolic or hyperbolic equations like ρ ε ∂ n u ε ∂ t n - div ( a ε ∇ u ε ) = f in Ω × ( 0 , T ) + boundary conditions , n ∈ { 1 , 2 } , when the coefficients ρ ε , a ε (defined in Ø ) take possibly high values on a ε -periodic set of grain-like inclusions of vanishing measure. Memory effects arise in the limit problem.

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...

Homogenization of thin piezoelectric perforated shells

Marius Ghergu, Georges Griso, Houari Mechkour, Bernadette Miara (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

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We rigorously establish the existence of the limit homogeneous constitutive law of a piezoelectric composite made of periodically perforated microstructures and whose reference configuration is a thin shell with fixed thickness. We deal with an extension of the Koiter shell model in which the three curvilinear coordinates of the elastic displacement field and the electric potential are coupled. By letting the size of the microstructure going to zero and by using the periodic unfolding...