Controllability properties of a partial differential equation (PDE) model describing a thermoelastic plate are studied. The PDE is composed of a Kirchoff plate equation coupled to a heat equation on a bounded domain, with the coupling taking place on the interior and boundary of the domain. The coupling in this PDE is parameterized by α > 0. Boundary control is exerted through the (two) free bo...

Periodic travelling waves are a fundamental solution form in oscillatory reactiondiffusion equations. Here I discuss the generation of periodic travelling waves in a reaction-diffusion system of the generic λ-ω form. I present numerical results suggesting that when this system is solved on a semi-infinite domain subject to Dirichlet boundary conditions in which the variables are fixed at zero, ...

singular perturbation problems have been studied by many mathematicians. since the approximate solutions of these problems are as the sum of internal solution (boundary layer area) and external ones, the formation or non-formation of boundary layers should be specified. this paper, investigates this issue for a singular perturbation problem including a first order differential equation with gen...

2014 We derive a model of convection appropriate for containers with large width to height ratios. It couples a real rapidly varying convective variable to a slowly varying « drift » velocity field given by its stream-function. The derivation assumes stress-free boundary conditions at the top and the bottom. We discuss its extension to the more realistic no-slip case and the analogies/differenc...

Using a weak convergence approach, we prove a LPD for the solution of 2D stochastic Navier Stokes equations when the viscosity converges to 0 and the noise intensity is multiplied by the square root of the viscosity. Unlike previous results on LDP for hydrodynamical models, the weak convergence is proven by tightness properties of the distribution of the solution in appropriate functional spaces.

where T ≥ 2 is a positive integer andΔu k u k 1 −u k is the forward difference operator. Throughout this paper, we denote by Z a, b the discrete interval {a, a 1, . . . , b}, where a and b are integers and a < b. We consider in 1.1 two different boundary conditions: a Dirichlet boundary condition u 0 0 and a Neumann boundary condition Δu T 0 . In the literature, the boundary condition considere...

The aim of this paper is to derive spectral and condition number estimates of the singlelayer operator for low-frequency multiple scattering problems. This work extends the analysis initiated in [6] to dense media. Estimates are obtained first in the case of circular cylinders by Fourier analysis and are next formally adapted to disks, ellipses and rectangles in the framework of boundary elemen...

In this work we deduce an explicit Sommerfeld-type radiation condition able to prove uniqueness for the problem of outgoing wave propagation in isotropic elastic half-spaces with free boundary condition. The expression is obtained by a rigorous asymptotic analysis of the Green’s function associated with this problem. Observe that this is an exterior problem with unbounded frontier. The main dif...

This note concerns a nonlinear differential equation problem in which both the nonlinearity in the equation and its solution are determined by prescribed data. The question under consideration arises from a study of two-dimensional steady parallel-flows of a perfect fluid governed by Euler’s equations and a free-boundary condition, when the distribution of vorticity is arbitrary but prescribed.

This work is devoted to stationary optimal control problems with polygonal constraints on the components of the state. Existence of Lagrange multipliers, of different regularity, is verified for the cases with and without Slater condition holding. For the numerical realization a semi-smooth Newton method is proposed for an appropriately chosen family of regularized problems. The asymptotic beha...