In this article, we study the hyperbolic problem K(x, t)utt − ∑n j=1 ( a(x, t)uxj ) + F (x, t, u,∇u) = 0 u = 0 on Γ1, ∂u ∂ν + β(x)ut = 0 on Γ0 u(0) = u, ut(0) = u 1 in Ω , where Ω is a bounded region in R whose boundary is partitioned into two disjoint sets Γ0,Γ1. We prove existence, uniqueness, and uniform stability of strong and weak solutions when the coefficients and the boundary conditions...

In the aim to find simplest and most efficient shape of a noise absorbing wall dissipate acoustical energy sound wave, we consider frequency model described by Helmholtz equation with damping on boundary. The well-posedness is shown in class domains $d$-set boundaries ($N-1\le d<N$). We introduce admissible Lipschitz boundaries, which an optimal exists following sense: prove existence Radon mea...

The natural frequencies and damping rates of surface waves in a circular cylinder with pinned-end boundary conditions are calculated in terms of the gravitational Reynolds and Bond numbers, C and B, and the slenderness of the cylinder A, in the limit C —>• 0. We consider higher-order approximations that include the effect of viscous dissipation in the Stokes boundary layers and the bulk. A comp...

In this paper, we are concerned with the boundary stabilization of two connected strings with middle joint anti-damping for which all eigenvalues of the (control) free system are located on the right complex plane. We first design an explicit state feedback controller to achieve exponential stability for the closedloop system. Consequently, we design the output feedback by using infinite-dimens...

We study the stability of the perfectly matched layer (PML) as a closure for the system of second order elastic wave equations in two space dimensions on the upper half–plane, −∞ < x < ∞, y ≥ 0. Using mode analysis, we analyze the stability of the PML initial boundary value problem on the half–plane. We consider in particular the free surface and Dirichlet boundary conditions, but the analysis ...

We study the boundary controllability problem for a multilayer Rao-Nakra sandwich beam. This beam model consists of a Rayleigh beam coupled with a number of wave equations. We consider all combinations of clamped and hinged boundary conditions with the control applied to either the moment or the rotation angle at an end of the beam. We prove that exact controllability holds provided the damping...

We describe Monte Carlo algorithms to solve elliptic partial differential equations with piecewise constant diffusion coefficients and general boundary conditions including Robin and transmission conditions as well as a damping term. The treatment of the boundary conditions is done via stochastic finite differences techniques which possess an higher order than the usual methods. The simulation ...

The attenuation of a plane acoustic wave incident on a flat impedance surface in a sheared and viscous fluid is investigated numerically and asymptotically. Predictions of various boundary models of impedance surfaces in shear flow are tested by comparing their predicted reflection coefficient. It is found that viscosity has a significant effect, reducing the reflection of upstream propagating ...

A new model for the interaction between the acoustic wave in an enclosed air cavity and the transversal motion of a flexible beam is proposed in this paper. This new boundary condition for the coupled wave and Euler-Bernoulli beam equations introduces sufficient damping of the energy of the system to gain uniform exponential stability. Careful physical justification of the boundary condition is...