Uniform stabilization for elastic waves system with highly nonlinear localized dissipation.
Uniform stabilization of a coupled structural acoustic system by boundary dissipation.
Uniform stabilization of some damped second order evolution equations with vanishing short memory
We consider a damped abstract second order evolution equation with an additional vanishing damping of Kelvin–Voigt type. Unlike the earlier work by Zuazua and Ervedoza, we do not assume the operator defining the main damping to be bounded. First, using a constructive frequency domain method coupled with a decomposition of frequencies and the introduction of a new variable, we show that if the limit system is exponentially stable, then this evolutionary system is uniformly − with respect to the calibration...
Uniformity and homogeneity of elastic rods, shells and Cosserat three-dimensional bodies.
Uniformity and homogeneity of elastic rods, shells and Cosserat three-dimensional bodies
We present a general geometrical theory of uniform bodies which includes three-dimensional Cosserat bodies, rods and shells as particular cases. Criteria of local homogeneity are given in terms on connections.
Unilateral contact applications using FEM software
Nonsmooth analysis, inequality constrained optimization and variational inequalities are involved in the modelling of unilateral contact problems. The corresponding theoretical and algorithmic tools, which are part of the area known as nonsmooth mechanics, are by no means classical. In general purpose software some of these tools (perhaps in a simplified way) are currently available. Two engineering applications, a rubber-coated roller contact problem and a masonry wall, solved with MARC, are briefly...
Unilateral contact of elastic bodies (moment theory).
Unilateral dynamic contact of von Kármán plates with singular memory
The solvability of the contact problem is proved provided the plate is simply supported. The singular memory material is assumed. This makes it possible to get a priori estimates important for the strong convergence of gradients of velocities of solutions to the penalized problem.
Unilateral elastic subsoil of Winkler's type: Semi-coercive beam problem
The mathematical model of a beam on a unilateral elastic subsoil of Winkler's type and with free ends is considered. Such a problem is non-linear and semi-coercive. The additional assumptions on the beam load ensuring the problem solvability are formulated and the existence, the uniqueness of the solution and the continuous dependence on the data are proved. The cases for which the solutions need not be stable with respect to the small changes of the load are described. The problem is approximated...
Unique global solvability of 1D Fried-Gurtin model
We investigate a 1-dimensional simple version of the Fried-Gurtin 3-dimensional model of isothermal phase transitions in solids. The model uses an order parameter to study solid-solid phase transitions. The free energy density has the Landau-Ginzburg form and depends on a strain, an order parameter and its gradient. The problem considered here has the form of a coupled system of one-dimensional elasticity and a relaxation law for a scalar order parameter. Under some physically justified assumptions...
Uniqueness in an inverse problem for an elasticity system.
Uniqueness of critical points for semi-linear Dirichlet problems in convex domains.
Uniqueness of the solution of the boundary-initial value problem for a linear elastic Cosserat continuum
Univalent -harmonic mappings : applications to composites
This paper is part of a larger project initiated with [2]. The final aim of the present paper is to give bounds for the homogenized (or effective) conductivity in two dimensional linear conductivity. The main focus is therefore the periodic setting. We prove new variational principles that are shown to be of interest in finding bounds on the homogenized conductivity. Our results unify previous approaches by the second author and make transparent the central role of quasiconformal mappings in all...
Univalent σ-harmonic mappings: applications to composites
This paper is part of a larger project initiated with [2]. The final aim of the present paper is to give bounds for the homogenized (or effective) conductivity in two dimensional linear conductivity. The main focus is therefore the periodic setting. We prove new variational principles that are shown to be of interest in finding bounds on the homogenized conductivity. Our results unify previous approaches by the second author and make transparent the central role of quasiconformal mappings in all...
Unstable simple modes for a class of Kirchhoff equations
Unsteady hydromagnetic free convection flow on a vertical infinite flat plate with suction