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Epitaxially strained elastic films: the case of anisotropic surface energies

Marco Bonacini (2013)

ESAIM: Control, Optimisation and Calculus of Variations

In the context of a variational model for the epitaxial growth of strained elastic films, we study the effects of the presence of anisotropic surface energies in the determination of equilibrium configurations. We show that the threshold effect that describes the stability of flat morphologies in the isotropic case remains valid for weak anisotropies, but is no longer present in the case of highly anisotropic surface energies, where we show that the flat configuration is always a local minimizer...

Non-smoothness in the asymptotics of thin shells and propagation of singularities. Hyperbolic case

Philippe Karamian, Jacqueline Sanchez-Hubert, Évariste Sanchez Palencia (2002)

International Journal of Applied Mathematics and Computer Science

We consider the limit behaviour of elastic shells when the relative thickness tends to zero. We address the case when the middle surface has principal curvatures of opposite signs and the boundary conditions ensure the geometrical rigidity. The limit problem is hyperbolic, but enjoys peculiarities which imply singularities of unusual intensity. We study these singularities and their propagation for several cases of loading, giving a somewhat complete description of the solution.

The energy method for elastic problems with non-homogeneous boundary conditions

Ramon Quintanilla (2002)

International Journal of Applied Mathematics and Computer Science

In this paper we propose the weighted energy method as a way to study estimates of solutions of boundary-value problems with non-homogeneous boundary conditions in elasticity. First, we use this method to study spatial decay estimates in two-dimensional elasticity when we consider non-homogeneous boundary conditions on the boundary. Some comments in the case of harmonic vibrations are considered as well. We also extend the arguments to a class of three-dimensional problems in a cylinder. A section...

Theoretical analysis of discrete contact problems with Coulomb friction

Tomáš Ligurský (2012)

Applications of Mathematics

A discrete model of the two-dimensional Signorini problem with Coulomb friction and a coefficient of friction depending on the spatial variable is analysed. It is shown that a solution exists for any and is globally unique if is sufficiently small. The Lipschitz continuity of this unique solution as a function of as well as a function of the load vector f is obtained. Furthermore, local uniqueness of solutions for arbitrary > 0 is studied. The question of existence of locally Lipschitz-continuous...

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