相关论文: Boundary controllability for the quasilinear wave …

In this paper we study the exact controllability problem for the wave equation on a finite metric graph with the Kirchhoff-Neumann matching conditions. Among all vertices and edges we choose certain active vertices and edges, and give a…

In this paper, we investigate the two-point boundary value problems for linear wave equation defined on a circle and prove that the equation possesses the exact controllability. We also investigate the two-point boundary value problems for…

By means of a direct and constructive method based on the theory of semiglobal $C^2$ solution, the local exact boundary observability is shown for nonautonomous 1-D quasilinear wave equations. The essential difference between nonautonomous…

Solutions of a system of wave equations are constructed for both homogeneous and inhomogeneous Dirichlet boundary conditions at every regularity level. We prove that boundary observability, and thus boundary exact controllability, at some…

We obtain sharp convergence rates, using Dirichlet correctors, for solutions of wave equations in a bounded domain with rapidly oscillating periodic coefficients. The results are used to prove the exact boundary controllability that is…

This paper establishes the local exact controllability of the quasilinear porous media equation with Dirichlet boundary condition.\\ Consider the equation $$\begin{aligned} &y_t - \Delta a(y) = mu+f \text{ on } Q\\ &y(0)=y_0,\ y…

In this paper we introduce some new concepts for second-order hyperbolic equations: two-point boundary value problem, global exact controllability and exact controllability. For several kinds of important linear and nonlinear wave equations…

We study the controllability of the multidimensional wave equation in a bounded domain with Dirichlet boundary condition, in which the support of the control is allowed to change over time. The exact controllability is reduced to the proof…

This paper is devoted to the study of the approximate controllability for a one-dimensional wave equation in domains with moving boundary. This equation models the motion of a string where an endpoint is fixed and the other one is moving.…

The problem of the exact bounded control of oscillations of the two-dimensional wave equation is considered. Control force is applied to the boundary of the membrane, which is located in a domain on a plane. The goal of the control is to…

We give a boundary observability result for a $1$d wave equation with a potential. We then deduce with a Schauder fixed-point argument the existence of a Neumann boundary control for a semi-linear wave equation $\partial_{tt}y -…

In this paper we establish several results on approximate controllability of a semilinear wave equation by making use of a single multiplicative control. These results are then applied to discuss the exact controllability properties for the…

The paper is devoted to the exact controllability of a system of coupled abstract wave equations when the control is exerted on a part of the boundary by means of one control. We give a Kalman type condition and give a description of the…

We study wave maps from the circle to a general compact Riemannian manifold. We prove that the global controllability of this geometric equation is characterized precisely by the homotopy class of the data. As a remarkable intermediate…

We consider the Linear Quadratic Regulation for the boundary control of the one dimensional linear wave equation under both Dirichlet and Neumann activation. For each activation we present a Riccati partial differential equation that we…

In this paper we establish the theory on semiglobal classical solution to first order quasilinear hyperbolic systems with a kind of nonlocal boundary conditions, and based on this, the corresponding exact boundary controllability and…

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…

In this paper, we deal with the boundary controllability of a one-dimensional degenerate and singular wave equation with degeneracy and singularity occurring at the boundary of the spatial domain. Exact boundary controllability is proved in…

We study the exact controllability for spatially periodic water waves with surface tension, by localized exterior pressures applied to free surfaces. We prove that in any dimension, the exact controllability holds within arbitrarily short…

The present article discusses the exact observability of the wave equation when the observation subset of the boundary is variable in time. In the one-dimensional case, we prove an equivalent condition for the exact observability, which…