Related papers: Exact Controllability and Stabilization of the Wav…
In this work, we solve the Euler's equations for periodic waves travelling under a sheet of ice using a reformulation introduced in Ablowitz et al. (2006). These waves are referred to as flexural-gravity waves. We compare and contrast two…
We will consider exact controllability of the distributed system governed by the wave equation with memory. It will be proved that this mechanical system can be driven to rest in finite time, the absolute value of the distributed control…
Direct observations of gravitational waves will open in the near future new windows on the Universe. Among the expected sources, instabilities of rotating compact astrophysical objects are waited to be detected with some impatience as this…
This paper deals with the controllability for a one-dimensional wave equation with mixed boundary conditions in a non-cylindrical domain. This equation models small vibrations of a string where an endpoint is fixed and the other is moving.…
These notes build an introduction to Convolution Quadrature techniques applied to linear convolutions and convolution equations with a bias to problems related to wave propagation. The notes are self-contained and emphasize algorithmic…
Based on a linear and non-linear study of radial pulsations in the envelopes of classical novae (Schenker 1999), I discuss the results both from the point of view of pulsation theory as well as their consequences for current nova models.…
In this work we study the orbital stability of periodic traveling-wave solutions for dispersive models. The study of traveling waves started in the mid-18th century when John S. Russel established that the flow of water waves in a shallow…
This paper deals with the boundary stabilization problem of a one-dimensional wave equation with a switching time-delay in the boundary. We show that the problem is well-posed in the sense of semigroups theory of linear operators. Then, we…
The authors of the paper "The third-order perturbed Korteweg-de Vries equation for shallow water waves with a non-flat bottom" [1] claim that they have derived the full third order perturbed KdV equation for the case of uneven bottom. We…
Controlling systems governed by partial differential equations is an inherently hard problem. Specifically, control of wave dynamics is challenging due to additional physical constraints and intrinsic properties of wave phenomena such as…
We consider a control system describing the interaction of water waves with a partially immersed rigid body constraint to move only in the vertical direction. The fluid is modeled by the shallow water equations. The control signal is a…
This paper deals with an analysis and design of robust, state-feedback control law uniform-asymptotically stabilizing at origin the system consisting of coupled $n$th--order ordinary differential equations in the presence of a non-vanishing…
The generation of ocean surface waves by wind is a classic fluid mechanics problem whose theoretical study dates back to 1957, when the two seminal papers by Phillips and Miles were published in the incipient Journal of Fluid Mechanics.…
Gravitational-wave astronomy will soon become a new tool for observing the Universe. Detecting and interpreting gravitational waves will require deep theoretical insights into astronomical sources. The past three decades have seen…
The paper presents a complete (to the best of the author's knowledge) overview on the existing literature concerning the NLS equation with point-concentrated nonlinearity. Precisely, it mainly covers the following topics: definition of the…
In order to improve the frequency dispersion effects of irrotational shallow water models in coastal oceanography, several full dispersion versions of classical models were formally derived in the literature. The idea, coming from G.…
In this paper we establish several results on approximate controllability of a semilinear wave equation by making use of a single multiplicative control. These results are then applied to discuss the exact controllability properties for the…
The emergence of nonequilibrium phenomena in individual complex wave systems has long been of fundamental interests. Its analytic studies remain notoriously difficult. Using the mathematical tool of the concentration of measure (CM), we…
These 1992 lectures notes present a powerful formalism mostly developed in the 1980s by Borderies, Goldreich and Tremaine to address planetary ring dynamical issues. These notes make a special emphasis on ring microphysics, quantified with…
In this paper, we establish some important results for the impulsive wave equation. We begin by proving the existence of a solution. Then, we study the impulse approximate controllability where the control function acts on a subdomain…