The search session has expired. Please query the service again.

Displaying 2081 – 2100 of 2633

Showing per page

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

Jiří Vala (2003)

Applications of Mathematics

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.

The nonlinear membrane model : a Young measure and varifold formulation

Med Lamine Leghmizi, Christian Licht, Gérard Michaille (2005)

ESAIM: Control, Optimisation and Calculus of Variations

We establish two new formulations of the membrane problem by working in the space of W Γ 0 1 , p ( Ω , 𝐑 3 ) -Young measures and W Γ 0 1 , p ( Ω , 𝐑 3 ) -varifolds. The energy functional related to these formulations is obtained as a limit of the 3 d formulation of the behavior of a thin layer for a suitable variational convergence associated with the narrow convergence of Young measures and with some weak convergence of varifolds. The interest of the first formulation is to encode the oscillation informations on the gradients minimizing sequences...

The nonlinear membrane model: a Young measure and varifold formulation

Med Lamine Leghmizi, Christian Licht, Gérard Michaille (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We establish two new formulations of the membrane problem by working in the space of W Γ 0 1 , p ( Ω , 𝐑 3 ) -Young measures and W Γ 0 1 , p ( Ω , 𝐑 3 ) -varifolds. The energy functional related to these formulations is obtained as a limit of the 3d formulation of the behavior of a thin layer for a suitable variational convergence associated with the narrow convergence of Young measures and with some weak convergence of varifolds. The interest of the first formulation is to encode the oscillation informations on the gradients minimizing...

The problem of dynamic cavitation in nonlinear elasticity

Jan Giesselmann, Alexey Miroshnikov, Athanasios E. Tzavaras (2012/2013)

Séminaire Laurent Schwartz — EDP et applications

The notion of singular limiting induced from continuum solutions (slic-solutions) is applied to the problem of cavitation in nonlinear elasticity, in order to re-assess an example of non-uniqueness of entropic weak solutions (with polyconvex energy) due to a forming cavity.

The regularisation of the N -well problem by finite elements and by singular perturbation are scaling equivalent in two dimensions

Andrew Lorent (2009)

ESAIM: Control, Optimisation and Calculus of Variations

Let K : = S O 2 A 1 S O 2 A 2 S O 2 A N where A 1 , A 2 , , A N are matrices of non-zero determinant. We establish a sharp relation between the following two minimisation problems in two dimensions. Firstly the N -well problem with surface energy. Let p 1 , 2 , Ω 2 be a convex polytopal region. Define I ϵ p u = Ω d p D u z , K + ϵ D 2 u z 2 d L 2 z and let A F denote the subspace of functions in W 2 , 2 Ω that satisfy the affine boundary condition D u = F on Ω (in the sense of trace), where F K . We consider the scaling (with respect to ϵ ) of m ϵ p : = inf u A F I ϵ p u . Secondly the finite element approximation to the N -well problem without surface...

The regularisation of the N-well problem by finite elements and by singular perturbation are scaling equivalent in two dimensions

Andrew Lorent (2008)

ESAIM: Control, Optimisation and Calculus of Variations

Let K : = S O 2 A 1 S O 2 A 2 S O 2 A N where A 1 , A 2 , , A N are matrices of non-zero determinant. We establish a sharp relation between the following two minimisation problems in two dimensions. Firstly the N-well problem with surface energy. Let p 1 , 2 , Ω 2 be a convex polytopal region. Define I ϵ p u = Ω d p D u z , K + ϵ D 2 u z 2 d L 2 z and let AF denote the subspace of functions in W 2 , 2 Ω that satisfy the affine boundary condition Du=F on Ω (in the sense of trace), where F K . We consider the scaling (with respect to ϵ) of m ϵ p : = inf u A F I ϵ p u . Secondly the finite element approximation to the N-well problem without...

Currently displaying 2081 – 2100 of 2633