Related papers: Energy Decay in a Wave Guide with Dissipation at I…
We study the linear wave equation on a class of spatially homogeneous and isotropic Friedmann-Lema\^itre-Robertson-Walker (FLRW) spacetimes in the decelerated regime with spatial topology $\mathbb{R}^3$. Employing twisted $t$-weighted…
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.
This paper aims to explore the long-term behavior of some nonlocal high-order-in-time wave equations. These equations, which have come to be known as Moore--Gibson--Thompson equations, arise in the context of acoustic wave propagation when…
In this paper we analyze a time-reversal experiment in a random underwater acoustic channel. In this kind of waveguide with semi-infinite cross section a propagating field can be decomposed over three kinds of modes: the propagating modes,…
We consider the wave equation in a bounded domain (eventually convex). Two kinds of inequality are described when occurs trapped ray. Applications to control theory are given. First, we link such kind of estimate with the damped wave…
We reconsider the refraction of evanescent waves at an interface between air and negative index medium under the assumption that negative index medium is necessarily dispersive and lossy. We show that all evanescent waves in air will be…
It is widely accepted that, on ensemble average, the transmission T of guided modes decays exponentially with the waveguide length L due to small imperfections, leading to the important figure of merit defined as the attenuation-rate…
Dissipation anomaly-the persistence of finite energy dissipation in the inviscid limit-is a hallmark of turbulence, sometimes regarded as the "zeroth law" of turbulent flows. Here, we demonstrate that this phenomenon is not exclusive to…
In this paper, we consider a wave equation with strong damping and logarithmic nonlinearity. This paper aims to study the local and global existence, uniqueness and the uniform energy decay rate of a weak solution under some sufficient…
We point out that even at the absolute zero of temperature environmental decoherence limits the destructive interference between time-reversed paths for an electron in a disordered metal, and thus causes the leading (`weak localization')…
We study the propagation properties of the solutions of the finite-difference space semi-discrete wave equation on an uniform grid of the whole Euclidean space. We provide a construction of high frequency wave packets that propagate along…
The aim of this note is to extend the energy decay estimates from [J. Wirth, J. Differential Equations 222 (2006) 487--514] to a broader class of time-dependent dissipation including very fast oscillations. This is achieved using…
The current work considers solutions to the wave equation on asymptotically flat, stationary, Lorentzian spacetimes in (1+3) dimensions. We investigate the relationship between the rate at which the geometry tends to flat and the pointwise…
This paper is concerned with decay estimate of solutions to the semilinear wave equation with strong damping in a bounded domain. Introducing an appropriate Lyaponuv function, we prove that when the damping is linear, we can find initial…
We study the rate of energy decay for solutions of a coupled wave-heat system on a rectangular domain. Using techniques from the theory of $C_0$-semigroups, and in particular a well-known result due to Borichev and Tomilov, we prove that…
We study the spectrum of the Helmholtz equation in a two-dimensional infinite waveguide, containing a weak heterogeneity localized at an internal point, and obeying Dirichlet boundary conditions at its border. We prove that, when the…
We study long range propagation of electromagnetic waves in random waveguides with rectangular cross-section and perfectly conducting boundaries. The waveguide is filled with an isotropic linear dielectric material, with randomly…
We consider the Cauchy problem for the wave equation in a general class of spherically symmetric black hole geometries. Under certain mild conditions on the far-field decay and the singularity, we show that there is a unique globally smooth…
In this article we prove a local energy estimate for the linear wave equation on metrics with slow decay to a Kerr metric with small angular momentum. As an application, we study the quasilinear wave equation $\Box_{g(u, t, x)} u = 0$ where…
New results for attenuation and damping of electromagnetic fields in rigid conducting media are derived under the conjugate influence of inertia due to charge carriers and displacement current. Inertial effects are described by a relaxation…