Related papers: Normality condition in elasticity
We consider the dynamics of point particles which are confined to a bounded, possibly nonconvex domain $\Omega$. Collisions with the boundary are described as purely elastic collisions. This turns the description of the particle dynamics…
This article aims to investigate sufficient conditions for the stability of stochastic differential equations with a random structure, particularly in contexts involving the presence of concentration points. The proof of asymptotic…
We study the quantitative stability of Serrin's symmetry problem and it's connection with a dynamic model for contact angle motion of quasi-static capillary drops. We prove a new stability result which is both linear and depends only on a…
This paper is concerned with the variational problem for the elastic energy defined on symmetric graphs under the unilateral constraint. Assuming that the obstacle function satisfies the symmetric cone condition, we prove (i) uniqueness of…
An unconstrained, non-linearly elastic, semi-infinite solid is maintained in a state of large static plane strain. A power-law relation between the pre-stretches is assumed and it is shown that this assumption is well-motivated physically…
We establish the relation between local stability of equilibria and slopes of critical curves for a specific class of difference equations. We then use this result to give global behavior results for nonnegative solutions of the system of…
Nonequilibrium dynamics at interfaces is generally driven by a chemical potential. Here we demonstrate a generic technique to derive the basic equations of motion, boundary conditions and the chemical potential in a consistent way from…
We examine whether fluctuation-induced forces can lead to stable levitation. First, we analyze a collection of classical objects at finite temperature that contain fixed and mobile charges, and show that any arrangement in space is unstable…
We derive a sufficient condition for stability in probability of an equilibrium of a randomly perturbed map in ${\mathbb R}^d$. This condition can be used to stabilize weakly unstable equilibria by random forcing. Analytical results on…
Motivated by networked systems, stochastic control, optimization, and a wide variety of applications, this work is devoted to systems of switching jump diffusions. Treating such nonlinear systems, we focus on stability issues. First…
In the field of soft dielectric elastomers, the notion electrostriction indicates the dependency of the permittivity on strain. The present paper is aimed at investigating the effects of electrostriction onto the stability behaviour of…
We show that the vibrational response of a glassy liquid at finite frequencies can be described by continuum mechanics despite the vast degeneracy of the vibrational ground state; standard continuum elasticity assumes a unique ground state.…
Localization of plastic strain induced by softening can be objectively described by a regularized plasticity model that postulates a dependence of the current yield stress on a nonlocal softening variable defined by a differential…
The goal of this paper is to investigate the stability of the Helmholtz equation in the high- frequency regime with non-smooth and rapidly oscillating coefficients on bounded domains. Existence and uniqueness of the problem can be proved…
In this paper we study a local and a non-local regularization of the system of nonlinear elastodynamics with a non-convex energy. We show that solutions of the non-local model converge to those of the local model in a certain regime. The…
We are interested in the question of stability in the field of shape optimization, with focus on the strategy using second order shape derivative. More precisely, we identify structural hypotheses on the hessian of the considered shape…
It is shown how the combination of atomic deposition and nonlinear diffusion may lead, below a critical temperature, to the growth of nonuniform layers on a substrate. The dynamics of such a system is of the Cahn-Hilliard type, supplemented…
This paper is devoted to the stabilization of the water-wave equations with surface tension through of an external pressure acting on a small part of the free surface. It is proved that the energy decays to zero exponentially in time,…
We prove a compactness and semicontinuity result that applies to minimisation problems in nonhomogeneous linear elasticity under Dirichlet boundary conditions. This generalises a previous compactness theorem that we proved and employed to…
Dielectric elastomers have recently been proposed for various biologically-relevant applications, in which they may operate in fluidic environments where surface tension effects may have a significant effect on their stability and…