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Displaying 81 –
100 of
441
This work deals with a two-dimensional inverse problem in the field of tomography. The geometry of an unknown inclusion has to be reconstructed from boundary measurements. In this paper, we extend previous results of R. Kress and his coauthors: the leading idea is to use the conformal mapping function as unknown. We establish an integrodifferential equation that the trace of the Riemann map solves. We write it as a fixed point equation and give conditions for contraction. We conclude with a series...
Recently several papers have related the production of sampling and interpolating sequences for multi-band signals to the solution of certain kinds of Wiener-Hopf equations. Our approach is based on connections between exponential Riesz bases and the controllability of distributed parameter systems. For the case of two-band signals we derive an operator whose invertibility is equivalent to the existence of a sampling and interpolating sequence, and prove the invertibility of this operator.
A control system of the second order in time with control
is considered. If the
system is controllable in a strong sense and
uT is the control
steering the system to the rest at time
T,
then the L2–norm of uT decreases as
while the –norm of uT is approximately constant.
The proof is based on the moment approach
and properties of the relevant exponential family. Results are
applied to the wave equation with boundary or distributed controls.
We consider a controllability problem for a beam, clamped at one boundary and
free at the other boundary, with an attached piezoelectric actuator. By
Hilbert Uniqueness Method (HUM)
and new results on diophantine approximations, we
prove that the space of exactly initial controllable data depends on the
location of the actuator. We also illustrate these results with numerical
simulations.
We consider the exact controllability problem
by boundary action
of hyperbolic systems of networks of Euler-Bernoulli beams.
Using the multiplier method and Ingham's inequality,
we give sufficient conditions insuring the exact controllability
for all time. These conditions are related to the spectral
behaviour of the associated operator and are sufficiently concrete
in order to be able to check them on particular networks
as illustrated on simple examples.
This paper focuses on the analytical properties of the
solutions to the continuity equation with non local flow. Our
driving examples are a supply chain model and an equation for the
description of pedestrian flows. To this aim, we prove the well
posedness of weak entropy solutions in a class of equations
comprising these models. Then, under further regularity conditions,
we prove the differentiability of solutions with respect to the
initial datum and characterize this derivative. A necessary
...
This paper focuses on the analytical properties of the
solutions to the continuity equation with non local flow. Our
driving examples are a supply chain model and an equation for the
description of pedestrian flows. To this aim, we prove the well
posedness of weak entropy solutions in a class of equations
comprising these models. Then, under further regularity conditions,
we prove the differentiability of solutions with respect to the
initial datum and characterize this derivative. A necessary
...
The control of the surface of water in a long canal by means of a wavemaker is investigated. The fluid motion is governed by the Korteweg-de Vries equation in lagrangian coordinates. The null controllability of the elevation of the fluid surface is obtained thanks to a Carleman estimate and some weighted inequalities. The global uncontrollability is also established.
The control of the surface of water in a long canal by
means of a wavemaker is investigated. The fluid motion is governed
by the Korteweg-de Vries equation in Lagrangian coordinates.
The null controllability of the elevation of the fluid surface
is obtained thanks to a Carleman estimate and some weighted inequalities.
The global uncontrollability is also established.
We study an initial boundary-value problem for a wave equation with time-dependent sound speed. In the control problem, we wish to determine a sound-speed function which damps the vibration of the system. We consider the case where the sound speed can take on only two values, and propose a simple control law. We show that if the number of modes in the vibration is finite, and none of the eigenfrequencies are repeated, the proposed control law does lead to energy decay. We illustrate the rich behavior...
We study an initial boundary-value problem for a wave
equation with time-dependent sound speed. In the control problem,
we wish to determine a sound-speed function which damps the
vibration of the system. We consider the case where the sound speed can
take on only two values, and propose a simple control law. We show
that if the number of modes in the vibration is finite, and none of
the eigenfrequencies are repeated, the proposed
control law does lead to energy decay. We illustrate the rich behavior
of...
We wish to show how the shock position in a nozzle could be controlled. Optimal control theory and algorithm is applied to the transonic equation. The difficulty is that the derivative with respect to the shock position involves a Dirac mass. The one dimensional case is solved, the two dimensional one is analyzed .
We wish to show how the shock position in a nozzle could be
controlled. Optimal control theory and algorithm is applied to the
transonic equation. The difficulty is that the derivative with
respect to the shock position involves a Dirac mass. The one
dimensional case is solved, the two dimensional one is analyzed .
Optimal design problems in mechanics can be mathematically formulated as optimal control tasks. The minimum principle is employed in solving such problems. This principle allows us to write down optimal design problems as Multipoint Boundary Value Problems (MPBVPs). The dimension of MPBVPs is an essential restriction that decides on numerical difficulties. Optimal control theory does not give much information about the control structure, i.e., about the sequence of the forms of the right-hand sides...
In this work, we examine the exact controllability of the solution of a linear elasticity system, with evolutive Ventcel's conditions, (see [3]), in a bounded domain of R3. We use the Hilbert uniqueness methode, (H.U.M), of J.L.Lions, (see [9]); some multipliers are defined on the boundary; the curvature tensor (see [6]), appears when computing some boundary integrals. This work can be inserted in the framework of the study of the exact controllability and stabilisation of various problems with...
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441