Related papers: Energy decay estimates for an axially travelling s…
We prove integrated local energy decay for solutions of the damped wave equation with time-dependent damping satisfying an appropriate generalization of the geometric control condition on asymptotically flat, stationary space-times. We…
We study the decay rate for the energy of solutions of a damped wave equation in a situation where the Geometric Control Condition is violated. We assume that the set of undamped trajectories is a flat torus of positive codimension and that…
We study the rate of decay of the energy functional of solutions of the wave equation with localized damping and a external force. We prove that the decay rates of the energy functional is determined from a forced differential equation.
We consider a beam-string-beam transmission problem, where two structurally damped or undamped beams are coupled with a frictionally damped string by transmission conditions. We show that for this type of structure, the dissipation produced…
Using the techniques of two dimensional conformal field theory we construct time dependent classical solutions in open string theory describing the decay of an unstable D-brane in the presence of background electric field, and explicitly…
This paper explores the exponential stability of two nonlinear wave equations coupled through their velocities. The analysis is divided into two main cases. First, we consider a system where one equation is damped, while the other…
Approximate formulas are derived to describe energy loss in a harmonic oscillator that experiences three distinct damping mechanisms: constant-magnitude (Coulomb), velocity-proportional (Stokes), and velocity-squared (Newton), using…
This paper revisits the problem of the string decay contribution to the axion cosmological energy density. We show that this contribution is proportional to the average relative increase when axion strings decay of a certain quantity…
We prove local and global energy decay for the wave equation in a wave guide with damping at infinity. More precisely, the absorption index is assumed to converge slowly to a positive constant, and we obtain the diffusive phenomenon typical…
We study the damped wave equation with a damping coefficient which is possibly singular and unbounded at infinity. In general, zero belongs to the spectrum of the corresponding generator, which prevents a uniform (exponential) decay for the…
We derive approximate expressions for the amplitude decay of harmonic oscillations weakly damped by the simultaneous action of three different damping forces: force of constant magnitude, force linear in velocity, and force quadratic in…
We consider the problem of energy decay rates for nonlinearly damped abstract infinite dimensional systems. We prove sharp, simple and quasi-optimal energy decay rates through an indirect method, namely a weak observability estimate for the…
Motivated by numerically modeling surface waves for inviscid Euler equations, we analyze linear models for damped water waves and establish decay properties for the energy for sufficiently regular initial configurations. Our findings give…
The properties of a one space-dimension, one particle dynamical system under the influence of a purely dissipative force are investigated. Assuming this force depends only on the velocity, it is demonstrated, in contrast to the case of…
We prove local and global energy decay for the asymptotically periodic damped wave equation on the Euclidean space. Since the behavior of high frequencies is already mostly understood, this paper is mainly about the contribution of low…
We study the toy model of interacting open and closed string tachyons which demonstrates some interesting properties of the unstable D-brane decay scenario. We compute a stress tensor of the system and study the energy and pressure…
The first article in a two-part series (the second article being [arXiv:2205.13197]) assumes a weak local energy decay estimate holds and proves that solutions to the linear wave equation with variable coefficients in $\mathbb R^{1+3}$,…
We study the global well-posedness and asymptotic behavior for a semilinear damped wave equation with Neumann boundary conditions, modelling a one-dimensional linearly elastic body interacting with a rigid substrate through an adhesive…
Starting from three-dimensional nonlinear elasticity under the restriction of incompressibility, we derive reduced models to capture the behavior of strings in response to external forces. Our $\Gamma$-convergence analysis of the…
We consider the transmission problem for a coupled system of undamped and structurally damped plate equations in two sufficiently smooth and bounded subdomains. It is shown that, independently of the size of the damped part, the damping is…