1,459 research outputs found
Logarithmic stabilization of the Euler-Bernoulli transmission plate equation with locally distributed Kelvin-Voigt damping
In this paper we will study the asymptotic behaviour of the energy decay of a
transmission plate equation with locally distributed Kelvin-Voigt feedback.
Precisly, we shall prove that the energy decay at least logarithmically over
the time. The originality of this method comes from the fact that using a
Carleman estimate for a transmission second order system which will be derived
from the plate equation to establish a resolvent estimate which provide, by the
famous Burq's result [Bur98], the kind of decay mentionned above.Comment: 16 pages, 1 figure. arXiv admin note: substantial text overlap with
arXiv:1301.353
Mean value property associated with the Dunkl Laplacian
Let be the Dunkl Laplacian on . The main goal of
this paper is to characterize -harmonic functions by means of a mean
value propertyComment: 10 page
Rapid exponential stabilization of a 1-D transmission wave equation with in-domain anti-damping
We consider the problem of pointwise stabilization of a one-dimensional wave
equation with an internal spatially varying anti-damping term. We design a
feedback law based on the backstepping method and prove exponential stability
of the closed-loop system with a desired decay rate.Comment: 15 page
Weak stabilization of a transmission Euler-Bernoulli plate equation with force and moment feedback
In this paper we will study the asymptotic behaviour of the energy decay of a
transmission plate equation with force and moment feedback. Precisly, we shall
prove that the energy decay at least logarithmically over the time. The method
consist to use the classical second order Carleman estimate to estabish a
resolvent estimate which provide by the famous Burq's result [Bur98] the kind
of decay above mentionned.Comment: 15 pages, 2 figure
Potential theory associated with the Dunkl Laplacian
The main goal of this paper is to give potential theoretical approach to
study the Dunkl Laplacian which is a standard example of
differential-difference operators. By introducing the Green kernel relative to
, we prove that the Dunkl Laplacian generates a balayage space and we
investigate the associated family of harmonic measures. Therefore, by mean of
harmonic kernels, we give a characterization of all -harmonic
functions on large class of open subsets of . We also
establish existence and uniqueness result of a solution of the corresponding
Dirichlet problem.Comment: 21 page
Energy decay estimates of elastic transmission wave/beam systems with a local Kelvin-Voigt damping
We consider a beam and a wave equations coupled on an elastic beam through
transmission conditions. The damping which is locally distributed acts through
one of the two equations only; its effect is transmitted to the other equation
through the coupling. First we consider the case where the dissipation acts
through the beam equation. Using a recent result of Borichev and Tomilov on
polynomial decay characterization of bounded semigroups we provide a precise
decay estimates showing that the energy of this coupled system decays
polynomially as the time variable goes to infinity. Second, we discuss the case
where the damping acts through the wave equation. Proceeding as in the first
case, we prove that this system is also polynomially stable and we provide
precise polynomial decay estimates for its energy. Finally, we show the lack of
uniform exponential decay of solutions for both models.Comment: 28 pages. arXiv admin note: text overlap with arXiv:1812.0592
A fast reconstruction algorithm for geometric inverse problems using topological sensitivity analysis and Dirichlet-Neumann cost functional approach
This paper is concerned with the detection of objects immersed in anisotropic
media from boundary measurements. We propose an accurate approach based on the
Kohn-Vogelius formulation and the topological sensitivity analysis method. The
inverse problem is formulated as a topology optimization one minimizing an
energy like functional. A topological asymptotic expansion is derived for the
anisotropic Laplace operator. The unknown object is reconstructed using a
level-set curve of the topological gradient. The efficiency and accuracy of the
proposed algorithm are illustrated by some numerical results. MOTS-CL\'ES :
Probl\`eme inverse g\'eom\'etrique, Laplace anisotrope, formulation de
Kohn-Vogelius, analyse de sensibilit\'e, optimisation topologique
Stabilization of fractional-evolution systems
This paper is devoted to the analysis of the problem of stabilization of
fractional (in time) partial differential equations. We consider the following
equation
with the initial data , where is a unbounded operator
in Hilbert space and stands for the fractional
derivative. We provide two main results concerning the behavior of the
solutions when . We look first to the case
where we prove that the solution of this problem is exponential stable then we
consider the case when we prove under some consideration on the
resolvent that the energy of the solution goes to as goes to the
infinity as
A non-iterative reconstruction method for an inverse problem modeled by a Stokes-Brinkmann equations
This article is concerned with the reconstruction of obstacle \O immersed
in a fluid flowing in a bounded domain in the two dimensional case. We
assume that the fluid motion is governed by the Stokes-Brinkmann equations. We
make an internal measurement and then have a least-square approach to locate
the obstacle. The idea is to rewrite the reconstruction problem as a topology
optimization problem. The existence and the stability of the optimization
problem are demonstrated. We use here the concept of the topological gradient
in order to determine the obstacle and it's rough location. The topological
gradient is computed using a straightforward way based on a penalization
technique without the truncation method used in the literature. The unknown
obstacle is reconstructed using a level-set curve of the topological gradient.
Finally, we make some numerical examples exploring the efficiency of the
method
Some constructions of multiplicative -ary Hom-Nambu algebras
We show that given a Hom-Lie algebra one can construct the n-ary Hom-Lie
bracket by means of an (n-2)-cochain of given Hom-Lie algebra and find the
conditions under which this n-ary bracket satisfies the Filippov-Jacobi
identity, there by inducing the structure of n-Hom-Lie algebra. We introduce
the notion of Hom-Lie -uplet system which is the generalization of Hom-Lie
triple system. We construct Hom-Lie -uplet system using a Hom-Lie algebra.Comment: arXiv admin note: text overlap with arXiv:1605.08281 by other author
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