Analytic controllability of the wave equation over a cylinder
Analytic controllability of the wave equation over a cylinder
We analyze the controllability of the wave equation on a cylinder when the control acts on the boundary, that does not satisfy the classical geometric control condition. We obtain precise estimates on the analyticity of reachable functions. As the control time increases, the degree of analyticity that is required for a function to be reachable decreases as an inverse power of time. We conclude that any analytic function can be reached if that control time is large enough. In the C∞ class, a...
Approximate controllability and its well-posedness for the semilinear reaction-diffusion equation with internal lumped controls
Approximate controllability and its well-posedness for the semilinear reaction-diffusion equation with internal lumped controls
We consider the one dimensional semilinear reaction-diffusion equation, governed in Ω = (0,1) by controls, supported on any subinterval of (0, 1), which are the functions of time only. Using an asymptotic approach that we have previously introduced in [9], we show that such a system is approximately controllable at any time in both L2(0,1)( and C0[0,1], provided the nonlinear term f = f(x,t, u) grows at infinity no faster than certain power of log |u|. The latter depends on the regularity...
Approximate controllability by birth control for a nonlinear population dynamics model
In this paper we analyse an approximate controllability result for a nonlinear population dynamics model. In this model the birth term is nonlocal and describes the recruitment process in newborn individuals population, and the control acts on a small open set of the domain and corresponds to an elimination or a supply of newborn individuals. In our proof we use a unique continuation property for the solution of the heat equation and the Kakutani-Fan-Glicksberg fixed point theorem.
Approximate controllability by birth control for a nonlinear population dynamics model
In this paper we analyse an approximate controllability result for a nonlinear population dynamics model. In this model the birth term is nonlocal and describes the recruitment process in newborn individuals population, and the control acts on a small open set of the domain and corresponds to an elimination or a supply of newborn individuals. In our proof we use a unique continuation property for the solution of the heat equation and the Kakutani-Fan-Glicksberg fixed point theorem.
Approximate controllability for a linear model of fluid structure interaction
Approximate controllability for a linear model of fluid structure interaction
We consider a linear model of interaction between a viscous incompressible fluid and a thin elastic structure located on a part of the fluid domain boundary, the other part being rigid. After having given an existence and uniqueness result for the direct problem, we study the question of approximate controllability for this system when the control acts as a normal force applied to the structure. The case of an analytic boundary has been studied by Lions and Zuazua in [9] where, in particular,...
Approximate controllability for a system of Schrödinger equations modeling a single trapped ion
Approximate controllability for systems described by right invertible operators
Approximate controllability of a hydro-elastic coupled system
Approximate controllability of a hydro-elastic coupled system
We analyze the controllability of the motion of a fluid by means of the action of a vibrating shell coupled at the boundary of the fluid. The model considered is linear. We study its approximate controllability, i.e. whether the fluid may reach a dense set of final configurations at a given time. We show that this problem can be reduced to a unique continuation question for the Stokes system. We prove that this unique continuation property holds generically among analytic domains and therefore,...
Approximate controllability of a reaction-diffusion system with a cross-diffusion matrix and fractional derivatives on bounded domains.
Approximate controllability of abstract discrete-time systems.
Approximate controllability of delayed semilinear control systems.
Approximate controllability of distributed systems by distributed controllers.
Approximate controllability of infinite dimensional systems of the n-th order
The objective of the article is to obtain general conditions for several types of controllability at once for an abstract differential equation of arbitrary order, instead of conditions for a fixed order equation. This innovative approach was possible owing to analyzing the n-th order linear system in the Frobenius form which generates a Jordan transition matrix of the Vandermonde form. We extensively used the fact that the knowledge of the inverse of a Jordan transition matrix enables us to directly...
Approximate controllability of neutral functional differential system with unbounded delay.
Approximate controllability of neutral stochastic integrodifferential systems in Hilbert spaces.
Approximate controllability of semilinear neutral systems in Hilbert spaces.