While the quasilinear isothermal Euler equations are an excellent model for gas pipeline flow, the operation of the pipeline flow with high pressure and small Mach numbers allows us to obtain approximate solutions by a simpler semilinear model. We provide a derivation of the semilinear model that shows that the semilinear model is valid for sufficiently low Mach numbers and sufficiently high pressures. We prove an existence result for continuous solutions of the semilinear model that takes into account lower and upper bounds for the pressure and an upper bound for the magnitude of the Mach number of the gas flow. These state constraints are important both in the operation of gas pipelines and to guarantee that the solution remains in the set where the model is physically valid. We show the constrained exact boundary controllability of the system with the same pressure and Mach number constraints.

We consider the linear wave equation with Dirichlet boundary conditions in a bounded interval, and with a control acting on a moving point. We give sufficient conditions on the trajectory of the control in order to have the exact controllability property.

Exact controllabilityresults for a multilayer plate system are obtained from the method of Carleman estimates.The multilayer plate system is a natural multilayer generalization of a classical three-layer “sandwichplate” system due to Rao and Nakra. The multilayer version involves a number ofLamé systems for plane elasticity coupled with a scalar Kirchhoff plate equation. The plate is assumed to be either clamped or hinged and controlsare assumed to be locally distributed in a neighborhood of a portion of the boundary. The Carleman estimates developed for thecoupled system are based on some new Carleman estimates for the Kirchhoff plate as well as some known Carleman estimates due to Imanuvilov and Yamamoto for the Lamé system.

We consider the numerical solution, in two- and three-dimensionalbounded domains, of the inverse problem for identifying the locationof small-volume, conductivity imperfections in a medium with homogeneousbackground. A dynamic approach, based on the wave equation, permitsus to treat the important case of “limited-view” data. Our numericalalgorithm is based on the coupling of a finite element solution ofthe wave equation, an exact controllability method and finally a Fourierinversion for localizing the centers of the imperfections. Numericalresults, in 2- and 3-D, show the robustness and accuracy of the approachfor retrieving randomly placed imperfections from both complete andpartial boundary measurements.

We study controllability for a nonhomogeneous string and ring under an axial stretchingtension that varies with time. We consider the boundary control for a string anddistributed control for a ring. For a string, we are looking for a controlf(t) ∈ L 2(0,T) that drives the state solution to rest. We show that for a ring, two forcesare required to achieve controllability. The controllability problem is reduced to amoment problem for the control. We describe the set of initial data which may be driven torest by the control. The proof is based on an auxiliary basis property result.

In this work we are interested in the study of controllability andstabilization of the linearized Benjamin-Ono equation withperiodic boundary conditions, which is a generic model forthestudy of weakly nonlinear waves with nonlocal dispersion. It iswell known that theBenjamin-Ono equation has infinite number ofconserved quantities, thus we consider only controls acting in theequation such that the volume of the solution is conserved. Westudy also the stabilization with a feedback law which gives us anexponential decay of the solutions.

This paper studies the exact controllability of the Maxwell system in a bounded domain, controlled by a current flowing tangentially in the boundary of the region, as well as the exact controllability the same problem but perturbed by a dissipative term multiplied by a small parameter in the boundary condition. This boundary perturbation improves the regularity of the problem and is therefore a singular perturbation of the original problem. The purpose of the paper is to examine the connection, for small values of the perturbation parameter, between observability estimates for the two systems, and between the optimality systems corresponding to the problem of norm minimum exact control of the solutions of the two systems from the rest state to a specified terminal state.

Consider a Timoshenko beam that is clamped to an axis perpendicular to the axis of the beam. We study the problem to move the beam from a given initial state to a position of rest, where the movement is controlled by the angular acceleration of the axis to which the beam is clamped. We show that this problem of controllability is solvable if the time of rotation is long enough and a certain parameter that describes the material of the beam is a rational number that has an even numerator and an odd denominator or vice versa.

We study the simultaneously reachable subspace for two strings controlled from a common endpoint. We give necessary and sufficient conditions for simultaneous spectral and approximate controllability. Moreover we prove the lack of simultaneous exact controllability and we study the space of simultaneously reachable states as a function of the position of the joint. For each type of controllability result we give the sharp controllability time.

We consider the exact controllability of a hybridsystem consisting of an elastic beam, clamped at one end and attached at the other end to arigid antenna. Such a system is governed by one partialdifferential equation and two ordinary differential equations. Using theHUM method, we prove that the hybrid system is exactlycontrollable in an arbitrarily short time in the usual energy space.

This essentially numerical study, sets out to investigate various geometrical properties of exact boundary controllability of the waveequation when the control is applied on a part of the boundary. Relationships between the geometry of the domain, the geometry ofthe controlled boundary, the time needed to control and the energy of the control are dealt with. A new norm of the control and anenergetic cost factor are introduced. These quantities enable a detailed appraisal of the numerical solutions obtained and the detectionof trapped rays.