Approximate controllability of a hydro-elastic coupled system

Approximate Controllability of a Hydro Elastic Coupled System Jacques Louis Lions and Enrique Zuazua

We analyze the controllability of the motion of a uid by means of the action of a vibrating shell coupled at the boundary of the uid The model considered is linear We study its approximate controllability i e whether the uid may reach a dense set of nal con gurations at a given time We show that this problem can be reduced to a unique continuation question for the Stokes system We prove that th...

Approximate controllability of a reaction-diffusion system

An open-loop control for a system coupling a reaction-diffusion system and an ordinary differential equation is proposed in this study. We use a flatness-like property, indeed, the solution can be expressed in terms of an infinite series depending on a flat output, its derivatives and its integrals. This series is shown to be convergent if the flat output is Gevrey of order 1 < a ≤ 2. Approxima...

Approximate controllability of the coupled degenerate system with two boundary controls

*Correspondence: [email protected] School of Basic Science, Changchun University of Technology, Changchun, 130012, P.R. China Abstract In this paper, we investigate the approximate controllability of the coupled system with boundary degeneracy. The control functions act on the degenerate boundary. We prove the Carleman estimate and the unique continuation of the adjoint system. Then we get the ...

Exact controllability of a system of coupled strings in parallel

A Hydro-elastic Model of Hydrocephalus

We combine elements of poroelasticity and of fluid mechanics to construct a mathematical model of the human brain and ventricular system. The model is used to study hydrocephalus, a pathological condition in which the normal flow of the cerebrospinal fluid is disturbed, causing the brain to become deformed. Our model extends recent work in this area by including flow through the aqueduct, by in...