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Displaying 21 –
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402
This paper studies the
exact controllability of a finite dimensional system obtained by
discretizing in space and time the linear 1-D wave system with a
boundary control at one extreme. It is known that usual schemes
obtained with finite difference or finite element methods are not
uniformly controllable with respect to the discretization
parameters h and Δt. We introduce an implicit finite
difference scheme which differs from the usual centered one by
additional terms of order h2 and Δt2. Using...
Here, we prove the uniform observability of a two-grid method for the semi-discretization of the -wave equation for a time ; this time, if the observation is made in , is optimal and this result improves an earlier work of Negreanu and Zuazua [C. R. Acad. Sci. Paris Sér. I 338 (2004) 413–418]. Our proof follows an Ingham type approach.
Here, we prove the uniform observability of a two-grid method
for the semi-discretization of the 1D-wave equation for a time ;
this time, if the observation is made in , is optimal and this result improves an earlier work of Negreanu and Zuazua [C. R. Acad. Sci. Paris Sér. I338 (2004) 413–418].
Our proof follows an Ingham type approach.
We analyze the controllability of the wave equation on a cylinder when the control acts on the
boundary, that does not satisfy the classical geometric control condition.
We obtain precise estimates on the analyticity of reachable functions.
As the control time increases, the degree of analyticity that is required for a function to
be reachable decreases as an inverse power of time.
We conclude that any analytic function can be reached if that control time is large enough.
In the C∞ class, a...
Computers are becoming sufficiently powerful to permit to numerically solve problems such as the wave equation with high-order methods. In this article we will consider Lagrange finite elementsof order k and show how it is possible to automatically generate the mass and stiffness matrices of any order with the help of symbolic computation software. We compare two high-order time discretizations: an explicit one using a Taylor expansion in time (a Cauchy-Kowalewski procedure) and an implicit Runge-Kutta...
We consider a hybrid, one-dimensional, linear system consisting
in two flexible strings connected by a point mass. It is known
that this system presents two interesting features. First, it is well
posed in an asymmetric space in which solutions have one more degree
of regularity to one side of the point mass. Second, that the spectral
gap vanishes asymptotically. We prove that the first property is a
consequence of the second one. We also consider a system in which the
point mass is replaced...
Let be the scattering matrix related to the wave equation in the exterior of a non-trapping obstacle , with Dirichlet or Neumann boundary conditions on . The function , called scattering phase, is determined from the equality . We show that has an asymptotic expansion as and we compute the first three coefficients. Our result proves the conjecture of Majda and Ralston for non-trapping obstacles.
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402