Related papers: Null Controllability for Wave Equations with Memor…
Gravitational wave memory is studied in the context of a certain class of braneworld wormholes. Unlike other wormhole geometries, this novel class of wormholes do not require any exotic matter fields for its traversability. First, we study…
In this paper, we study several theoretical and numerical questions concerning the null controllability problems for linear parabolic equations and systems for several dimensions. The control is distributed and acts on a small subset of the…
The gravitational wave memory effect is characterized by the permanent relative displacement of a pair of initially comoving test particles that is caused by the passage of a burst of gravitational waves. Recent research on this effect has…
We prove the null controllability of a one-dimensional degenerate parabolic equation with drift and a singular potential. Here, we consider a weighted Neumann boundary control at the left endpoint, where the potential arises. We use a…
The paper is devoted to the controllability problem for 3D compressible Euler system. The control is a finite-dimensional external force acting only on the velocity equation. We show that the velocity and density of the fluid are…
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…
We establish the null controllability for linear stochastic fourth order parabolic equations. Utilizing the duality argument, the null controllability is reduced to the observability for backward fourth order stochastic parabolic equations,…
The paper deals with exact null-controllability problem for a linear control system consisting of two serially connected abstract control systems. Controllability conditions are obtained. Applications to the exact null-controllability for…
In this article we study a controllability problem for a parabolic and a hyperbolic partial differential equations in which the control is the shape of the domain where the equation holds. The quantity to be controlled is the trace of the…
We consider the wave equation in a bounded domain (eventually convex). Two kinds of inequality are described when occurs trapped ray. Applications to control theory are given. First, we link such kind of estimate with the damped wave…
In this paper, we present a null controllability result for a class of stochastic semi-discrete parabolic equations. For this purpose, an observability estimate is established for backward stochastic semi-discrete parabolic equations, with…
We study the null-controllability of parabolic equations associated to non-autonomous Ornstein-Uhlenbeck operators. When a Kalman type condition holds for some positive time $T>0$, these parabolic equations are shown to enjoy a Gevrey…
We prove the interior null-controllability of one-dimensional parabolic equations with time independent measurable coefficients.
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…
In this paper we establish an observability inequality for the heat equation with bounded potentials on the whole space. Roughly speaking, such a kind of inequality says that the total energy of solutions can be controlled by the energy…
This paper is devoted to studying null controllability for a class of stochastic fourth order semi-discrete parabolic equations, where the spatial variable is discretized with finite difference scheme and the time is kept as a continuous…
For abstract linear systems in Hilbert spaces we revisit the problems of exact controllability and complete stabilizability (stabilizability with an arbitrary decay rate), the latter property is equivalent to exact null controllability. We…
In this paper, we continue the study of some controllability issues for the forward stochastic heat equation with dynamic boundary conditions. The main novelty in the present paper consists of considering only one control without extra…
We examine a simple example of gravitational wave memory due to the decay of a point particle into two point particles. In the case where one of the decay products is null, there are two types of memory: a null memory due to the null…
We propose a numerical method to approximate the exact averaged boundary control of a family of wave equations depending on an unknown parameter sigma. More precisely the control, independent of sigma, that drives an initial data to a…