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Numerical mathematics
, 2000
"... Abstract. In this paper we introduce some basic differential models for the description of blood flow in the circulatory system. We comment on their mathematical properties, their meaningfulness and their limitation to yield realistic and accurate numerical simulations, and their contribution for a ..."
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Abstract. In this paper we introduce some basic differential models for the description of blood flow in the circulatory system. We comment on their mathematical properties, their meaningfulness and their limitation to yield realistic and accurate numerical simulations, and their contribution for a better understanding of cardiovascular physiopathology. Mathematics Subject Classification (2000). 92C50,96C10,76Z05,74F10,65N30,65M60. Keywords. Cardiovascular mathematics; mathematical modeling; fluid dynamics; Navier– Stokes equations; numerical approximation; finite element method; differential equations. 1.
Local controllability of a 1D tank containing a fluid modeled by the shallow water equations
 ESAIM: COCV
, 2002
"... Abstract. We consider a 1D tank containing an inviscid incompressible irrotational fluid. The tank is subject to the control which consists of horizontal moves. We assume that the motion of the fluid is welldescribed by the Saint–Venant equations (also called the shallow water equations). We prove ..."
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Cited by 44 (15 self)
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Abstract. We consider a 1D tank containing an inviscid incompressible irrotational fluid. The tank is subject to the control which consists of horizontal moves. We assume that the motion of the fluid is welldescribed by the Saint–Venant equations (also called the shallow water equations). We prove the local controllability of this nonlinear control system around any steady state. As a corollary we get that one can move from any steady state to any other steady state.
The squares of the LaplacianDirichlet eigenfunctions are generically linearly independent
 in "ESAIM Control
, 2009
"... ABSTRACT. The paper deals with the genericity of domaindependent spectral properties of the LaplacianDirichlet operator. In particular we prove that, generically, the squares of the eigenfunctions form a free family. We also show that the spectrum is generically nonresonant. The results are obtai ..."
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Cited by 22 (6 self)
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ABSTRACT. The paper deals with the genericity of domaindependent spectral properties of the LaplacianDirichlet operator. In particular we prove that, generically, the squares of the eigenfunctions form a free family. We also show that the spectrum is generically nonresonant. The results are obtained by applying global perturbations of the domains and exploiting analytic perturbation properties. The work is motivated by two applications: an existence result for the problem of maximizing the rate of exponential decay of a damped membrane and an approximate controllability result for the bilinear Schrödinger equation.
On conditions that prevent steadystate controllability of certain linear partial differential equations. Discrete Contin
 Dyn. Syst
"... Abstract. In this paper, we investigate the connections between controllability properties of distributed systems and existence of non zero entire functions subject to restrictions on their growth and on their sets of zeros. Exploiting these connections, we first show that, for generic bounded open ..."
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Cited by 7 (3 self)
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Abstract. In this paper, we investigate the connections between controllability properties of distributed systems and existence of non zero entire functions subject to restrictions on their growth and on their sets of zeros. Exploiting these connections, we first show that, for generic bounded open domains in dimension n ≥ 2, the steady–state controllability for the heat equation with boundary controls dependent only on time, does not hold. In a second step, we study a model of a water tank whose dynamics is given by a wave equation on a twodimensional bounded open domain. We provide a condition which prevents steady–state controllability of such a system, where the control acts on the boundary and is only dependent on time. Using that condition, we prove that the steady–state controllability does not hold for generic tank shapes. 1. Introduction. We
Approximate controllability for a linear model of fluid structure interaction
 ESAIM: Contr. Optim. Calc. Var
, 1999
"... Abstract. 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 a ..."
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Cited by 6 (0 self)
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Abstract. 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, a counterexample is given when the fluid domain is a ball. We prove a result of approximate controllability in the 2dcase when the rigid and the elastic parts of the boundary make a rectangular corner and if the control acts on the whole elastic structure. Resume. Nous considerons un modele lineaire d’interaction entre un fluide visqueux incompressible et une structure elastique mince situee sur une partie de la frontiere du domaine fluide, l’autre partie de la frontiere etant rigide. Apres avoir donne un resultat d’existence et d’unicite pour le probleme direct, nous etudions la question de la contrôlabilite approchee pour ce systeme lorsque le contrôle agit comme une force normale appliquee a la structure. Le cas d’une frontiere analytique a ete etudie par Lions et Zuazua dans [9] ou, en particulier, un contre exemple est donne lorsque le domaine fluide est une boule. Nous montrons un resultat de contrôlabilite approchee dans le cas 2d quand les parties rigide et elastique de la frontiere forment un angle droit et si le contrôle agit sur toute la structure
ftp ejde.math.txstate.edu (login: ftp) POSITIVE PERIODIC SOLUTIONS OF NEUTRAL LOGISTIC EQUATIONS WITH DISTRIBUTED DELAYS
"... Abstract. Using a fixed point theorem of strictsetcontraction, we establish criteria for the existence of positive periodic solutions for the periodic neutral logistic equation, with distributed delays, x ′ h nX Z 0 mX ..."
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Abstract. Using a fixed point theorem of strictsetcontraction, we establish criteria for the existence of positive periodic solutions for the periodic neutral logistic equation, with distributed delays, x ′ h nX Z 0 mX
EXACT CONTROLLABILITY OF AN ELASTIC MEMBRANE COUPLED WITH A POTENTIAL FLUID
"... We consider the problem of boundary control of an elastic system with coupling to a potential equation. The potential equation represents the linearized motions of an incompressible inviscid fluid in a cavity bounded in part by an elastic membrane. Sufficient control is placed on a portion of the el ..."
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We consider the problem of boundary control of an elastic system with coupling to a potential equation. The potential equation represents the linearized motions of an incompressible inviscid fluid in a cavity bounded in part by an elastic membrane. Sufficient control is placed on a portion of the elastic membrane to insure that the uncoupled membrane is exactly controllable. The main result is that if the density of the fluid is sufficiently small, then the coupled system is exactly controllable.
Exact Controllability of a SecondOrder IntegroDifferential Equation with a Pressure Term
"... Abstract. This paper is concerned with the boundary exact controllability of the equation u ′ ′ ∫ t − ∆u − g(t − σ)∆u(σ)dσ = −∇p 0 where Q is a finite cylinder Ω×]0, T [ , Ω is a bounded domain of R n, u = (u1(x, t), · · · , u2(x, t)), x = (x1, · · · , xn) are n − dimensional vectors and p de ..."
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Abstract. This paper is concerned with the boundary exact controllability of the equation u ′ ′ ∫ t − ∆u − g(t − σ)∆u(σ)dσ = −∇p 0 where Q is a finite cylinder Ω×]0, T [ , Ω is a bounded domain of R n, u = (u1(x, t), · · · , u2(x, t)), x = (x1, · · · , xn) are n − dimensional vectors and p denotes a pressure term. The result is obtained by applying HUM (Hilbert Uniqueness Method) due to J.L.Lions. The above equation is a simple model of dynamical elasticity equations for incompressible materials with memory.