Displaying similar documents to “On the precise asymptotics of the constant in Friedrich's inequality for functions vanishing on the part of the boundary with microinhomogeneous structure.”

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.

Junction of elastic plates and beams

Antonio Gaudiello, Régis Monneau, Jacqueline Mossino, François Murat, Ali Sili (2007)

ESAIM: Control, Optimisation and Calculus of Variations

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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 ε . The lateral boundary of the plate and the top of the beam are assumed to be clamped. When and r ε tend to zero simultaneously, with r ε ≫ ε 2 , we identify the limit problem. This limit problem involves six junction conditions.