We give a necessary and sufficient condition, of geometrical type, for the uniform decay of energy of solutions of the linear system of magnetoelasticity in a bounded domain with smooth boundary. A Dirichlet-type boundary condition is assumed. When the geometrical condition is not fulfilled, we show polynomial decay of the energy, for smooth initial conditions. Our strategy is to use micro-loca...

Part 2 continues the study of optimization techniques for elliptic control problems subject to control and state constraints and is devoted to distributed control. Boundary conditions are of mixed Dirichlet and Neumann type. Necessary conditions of optimality are formally stated in form of a local Pontryagin minimum principle. By introducing suitable discretization schemes, the control problem ...

We consider the imposition of Dirichlet boundary conditions in the finite element modelling of moving boundary problems in one and two dimensions for which the total mass is prescribed. A modification of the standard linear finite element test space allows the boundary conditions to be imposed strongly whilst simultaneously conserving a discrete mass. The validity of the technique is assessed f...

We consider the Stokes and Navier–Stokes equations with boundary conditions of Dirichlet type on the velocity on one part of the boundary and involving the pressure on the rest of the boundary. We write the variational formulations of such problems. Next we propose a finite element discretization of them and perform the a priori and a posteriori analysis of the discrete problem. Some numerical ...

Various methods for treating nonhomogeneous Dirichlet boundary conditions for the p-version of the finite element method are presented. These methods are theoretically and comrutationally analyzed. Numerical experimentations are given. They clearly illustrate the importance of the right treatment of the nonhomogeneous Dirichlet boundary conditions.

This paper deals with the Klein-Gordon-Maxwell system in a bounded spatial domain. We study the existence of solutions having a specific form, namely standing waves in equilibrium with a purely electrostatic field. We prescribe Dirichlet boundary conditions on the matter field, and either Dirichlet or Neumann boundary conditions on the electric potential. MSC2000: 35J55, 35J65, 35J50, 35Q40, 35...

In the context of the bulk-boundary correspondence we study the correlation functions arising on a boundary for different types of boundary conditions. The most general condition is the mixed one interpolating between the Neumann and Dirichlet conditions. We obtain the general expressions for the correlators on a boundary in terms of Green’s function in the bulk for the Dirichlet, Neumann and m...

Dromions are exponentially localised coherent structures supported by nonlinear integrable evolution equations in two spatial dimensions. In the study of initial-value problems on the plane, such solutions occur only if one imposes nontrivial boundary conditions at infinity, a situation of dubious physical significance. However it is established here that dromions appear naturally in the study ...

We calculate radiative corrections to the Casimir effect for the massive complex scalar field with the λφ4 self-interaction in d + 1 dimensions. We consider the field submitted to four types of boundary conditions on two parallel planes, namely: (i) quasi-periodic boundary conditions, which interpolates continuously periodic and anti-periodic ones, (ii) Dirichlet conditions on both planes, (iii...

In this paper we are concerned with deblurring problems in the case of multiple images coming from the Large Binocular Telescope (an important example of telescope of interferometric type). For this problem we are interested in checking the role of the boundary conditions in the quality of the reconstructed image. In particular we will consider reflective and anti-reflective boundary conditions...