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First, we consider a semilinear hyperbolic equation with a locally distributed damping in a bounded domain. The damping is located on a neighborhood of a suitable portion of the boundary. Using a Carleman estimate [Duyckaerts, Zhang and Zuazua, Ann. Inst. H. Poincaré Anal. Non Linéaire (to appear); Fu, Yong and Zhang, SIAM J. Contr. Opt. 46 (2007) 1578–1614], we prove that the energy of this system decays exponentially to zero as the time variable goes to infinity. Second, relying on another Carleman...
First, we consider a semilinear hyperbolic equation with a
locally distributed damping in a bounded
domain. The damping is located on a neighborhood of a suitable portion of the
boundary. Using a Carleman estimate [Duyckaerts, Zhang and Zuazua, Ann. Inst. H. Poincaré Anal. Non Linéaire (to appear); Fu, Yong and Zhang, SIAM J. Contr. Opt.46 (2007) 1578–1614], we prove that the energy of this system decays exponentially to zero as the time variable goes to infinity. Second, relying on another Carleman...
This work considers a Bresse system with viscoelastic damping on the vertical displacement and heat conduction effect on the shear angle displacement. A general stability result with minimal condition on the relaxation function is obtained. The system under investigation, to the best of our knowledge, is new and has not been studied before in the literature. What is more interesting is the fact that our result holds without the imposition of the equal speed of wave propagation condition, and differentiation...
We also exhibit a set of localized data for which the corresponding solutions are strongly focused, which in geometric terms means that a wave travels along an specific incoming null geodesic in such a way that almost all of the energy is concentrated in a tubular neighborhood of the geodesic and almost no energy radiates out of this neighborhood.
In this article we give a construction of the wave group for variable coefficient, time dependent wave equations, under the hypothesis that the coefficients of the principal term possess two bounded derivatives in the spatial variables, and one bounded derivative in the time variable. We use this construction to establish the Strichartz and Pecher estimates for solutions to the Cauchy problem for such equations, in space dimensions and .
We prove a sharp bilinear estimate for the wave equation from which we obtain the sharp constant in the Strichartz estimate which controls the norm of the solution in terms of the energy. We also characterise the maximisers.
The aim of this paper is to answer the question: Do the controls of a vanishing viscosity approximation of the one dimensional linear wave equation converge to a control of the conservative limit equation? The characteristic of our viscous term is that it contains the fractional power α of the Dirichlet Laplace operator. Through the parameter α we may increase or decrease the strength of the high frequencies damping which allows us to cover a large class of dissipative mechanisms. The viscous term,...
One of the important issues on the distribution network design is to incorporate
inventory management cost into the facility location model. This paper deals with a
network model making the decisions on the facility location such as the number of DCs and
their locations as well as the decisions on the inventory management such as the ordering
quantity and the level of safety stock at each DC. The considered model differs from the
previous works by...
One of the important issues on the distribution network design is to incorporate
inventory management cost into the facility location model. This paper deals with a
network model making the decisions on the facility location such as the number of DCs and
their locations as well as the decisions on the inventory management such as the ordering
quantity and the level of safety stock at each DC. The considered model differs from the
previous works by...
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 and . We introduce an implicit finite difference scheme which differs from the usual centered one by additional terms of order and . Using a discrete...
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