Controllability of a viscoelastic plate using one boundary control in displacement or bending

In this paper we consider a viscoelastic plate (linear viscoelasticity of the Maxwell-Boltzmann type) and we compare its controllability properties with the (known) controllability of a purely elastic plate (the control acts on the boundary displacement or bending). By combining operator and moment methods, we prove that the viscoelastic plate inherits the controllability properties of the purely elastic plate

Modelling and Inverse Problems of Control for Distributed Parameter Systems; Proceedings of IFIP(W.G. 7.2)-IIASA Conference, July 24-28, 1989

The techniques of solving inverse problems that arise in the estimation and control of distributed parameter systems in the face of uncertainty as well as the applications of these to mathematical modelling for problems of applied system analysis (environmental issues, technological processes, biomathematical models, mathematical economy and other fields) are among the major topics of research at the Dynamic Systems Project of the Systems and Decision Sciences (SDS) Program at IIASA. In July 1989 the SDS Program was a coorganizer of a regular IFIP (WG 7.2) conference on Modelling and Inverse Problems of Control for Distributed Parameter Systems that was held at IIASA, and was attended by a number of prominent theorists and practitioners. One of the main purpose of this meeting was to review recent developments and perspectives in this field. The proceedings are presented in this volume

Thermoacoustic tomography with an arbitrary elliptic operator

Thermoacoustic tomography is a term for the inverse problem of determining of one of initial conditions of a hyperbolic equation from boundary measurements. In the past publications both stability estimates and convergent numerical methods for this problem were obtained only under some restrictive conditions imposed on the principal part of the elliptic operator. In this paper logarithmic stability estimates are obatined for an arbitrary variable principal part of that operator. Convergence of the Quasi-Reversibility Method to the exact solution is also established for this case. Both complete and incomplete data collection cases are considered.Comment: 16 page

Dynamics of thermoelastic thin plates: A comparison of four theories

Four distinct theories describing the flexural motion of thermoelastic thin plates are compared. The theories are due to Chadwick, Lagnese and Lions, Simmonds, and Norris. Chadwick's theory requires a 3D spatial equation for the temperature but is considered the most accurate as the others are derivable from it by different approximations. Attention is given to the damping of flexural waves. Analytical and quantitative comparisons indicate that the Lagnese and Lions model with a 2D temperature equation captures the essential features of the thermoelastic damping, but contains systematic inaccuracies. These are attributable to the approximation for the first moment of the temperature used in deriving the Lagnese and Lions equation. Simmonds' model with an explicit formula for temperature in terms of plate deflection is the simplest of all but is accurate only at low frequency, where the damping is linearly proportional to the frequency. It is shown that the Norris model, which is almost as simple as Simmond's, is as accurate as the more precise but involved theory of Chadwick.Comment: 2 figures, 1 tabl

Thermoacoustic tomography with variable sound speed

We study the mathematical model of thermoacoustic tomography in media with a variable speed for a fixed time interval, greater than the diameter of the domain. In case of measurements on the whole boundary, we give an explicit solution in terms of a Neumann series expansion. We give necessary and sufficient conditions for uniqueness and stability when the measurements are taken on a part of the boundary

Well-posedness of boundary layer equations for time-dependent flow of non-Newtonian fluids

We consider the flow of an upper convected Maxwell fluid in the limit of high Weissenberg and Reynolds number. In this limit, the no-slip condition cannot be imposed on the solutions. We derive equations for the resulting boundary layer and prove the well-posedness of these equations. A transformation to Lagrangian coordinates is crucial in the argument

Reconstructing initial data using observers: error analysis of the semi-discrete and fully discrete approximations

A new iterative algorithm for solving initial data inverse problems from partial observations has been recently proposed in Ramdani et al. (Automatica 46(10), 1616-1625, 2010 ). Based on the concept of observers (also called Luenberger observers), this algorithm covers a large class of abstract evolution PDE's. In this paper, we are concerned with the convergence analysis of this algorithm. More precisely, we provide a complete numerical analysis for semi-discrete (in space) and fully discrete approximations derived using finite elements in space and an implicit Euler method in time. The analysis is carried out for abstract Schrödinger and wave conservative systems with bounded observation (locally distributed)

A variational approach to strongly damped wave equations

We discuss a Hilbert space method that allows to prove analytical well-posedness of a class of linear strongly damped wave equations. The main technical tool is a perturbation lemma for sesquilinear forms, which seems to be new. In most common linear cases we can furthermore apply a recent result due to Crouzeix--Haase, thus extending several known results and obtaining optimal analyticity angle.Comment: This is an extended version of an article appeared in \emph{Functional Analysis and Evolution Equations -- The G\"unter Lumer Volume}, edited by H. Amann et al., Birkh\"auser, Basel, 2008. In the latest submission to arXiv only some typos have been fixe