相关论文: On boundary controllability and stabilizability of…

In this paper we consider an interior stabilization problem for the wave equation with dynamic boundary delay.We prove some stability results under the choice of damping operator. The proof of the main result is based on a frequency domain…

This paper is devoted to the exponential stability for one-dimensional linear wave equations with in-domain localized damping and several types of Wentzell (or dynamic) boundary conditions. In a quite general boundary setting, we establish…

I have applied multiple-scale perturbation theory to a generalized complex $PT$-symmetric Mathieu equation in order to find the stability boundaries between bounded and unbounded solutions. The analysis suggests that the non-Hermitian…

The evolution problem for a quantum particle confined in a 1D box and interacting with one fixed point through a time dependent point interaction is considered. Under suitable assumptions of regularity for the time profile of the…

We study the wave equation in an interval with two linearly moving endpoints. We give the exact solution by a series formula, then we show that the energy of the solution decay at the rate $1/t$. We also establish observability results, at…

We investigate a two-dimensional transmission model consisting of a wave equation and a Kirchhoff plate equation with dynamical boundary controls under geometric conditions. The two equations are coupled through transmission conditions…

The stability and transition in the bottom boundary layer under a solitary wave are analysed in the presence of finite amplitude disturbances. First, the receptivity of the boundary layer is investigated using a linear input-output…

The rotated multipliers method is performed in the case of the boundary stabilization by means of a(linear or non-linear) Neumann feedback. this method leads to new geometrical cases concerning the "active" part of the boundary where the…

We discuss boundary control of a wave equation with a non-linear anti-damping boundary condition. We design structured finite-dimensional $H_\infty$-output feedback controllers which stabilize the infinite dimensional system exponentially…

We consider a degenerate wave equation in one dimension, with drift and in presence of a leading operator which is not in divergence form. We impose a homogeneous Dirichlet boundary condition where the degeneracy occurs and a boundary…

This work is concerned with the possibility of proving the boundary null controllability for the degenerate wave equation, developing the asymptotic analysis of a suitable family of state-control pairs $((u_\varepsilon ,…

We propose a spectral collocation method to approximate the exact boundary control of the wave equation in a square domain. The idea is to introduce a suitable approximate control problem that we solve in the finite-dimensional space of…

In this paper, we are concerned with the study of stabilization problem for the following strongly degenerate wave equation in one space dimension $$w_{tt}(x,t)-\left(x^\alpha w_x(x,t)\right)_x=0$$ where ${\bf\alpha\in [1,2)}$. Thus, using…

The goal of this work is to compute a boundary control of reaction-diffusion partial differential equation. The boundary control is subject to a constant delay, whereas the equation may be unstable without any control. For this system…

An approach for shielding an unwanted wave with a fixed frequency by generating a suitably controlled nontrivial wave with the same frequency is suggested. Unlike the well known surface potential approach, the source of the controlled wave…

The paper is concerned with the boundary controllability of entropy weak solutions to hyperbolic systems of conservation laws. We prove a general result on the asymptotic stabilization of a system near a constant state. On the other hand,…

In this paper, we study the indirect boundary stability and exact controllability of a one-dimensional Timoshenko system. In the first part of the paper, we consider the Timoshenko system with only one boundary fractional damping. We first…

This thesis is concerned with dynamics of conservative nonlinear waves on bounded domains. In general, there are two scenarios of evolution. Either the solution behaves in an oscillatory, quasiperiodic manner or the nonlinear effects cause…

We address the exact boundary controllability of the semilinear wave equation $\partial_{tt}y-\Delta y + f(y)=0$ posed over a bounded domain $\Omega$ of $\mathbb{R}^d$. Assuming that $f$ is continuous and satisfies the condition…

We study the boundary exact controllability for the quasilinear wave equation in the higher-dimensional case. Our main tool is the geometric analysis. We derive the existence of long time solutions near an equilibrium, prove the locally…