Related papers: On pointwise decay of waves
The coherent control of wave absorption has important applications in areas such as energy harvesting, imaging, and sensing. However, most practical scenarios involve the absorption of partially coherent rather than fully coherent waves.…
New parameterizations for the spectra dissipation of wind-generated waves are proposed. The rates of dissipation have no predetermined spectral shapes and are functions of the wave spectrum and wind speed and direction, in a way consistent…
We determine the phase portrait of a Hamiltonian system of equations describing the motion of the particles in linear deep-water waves. The particles experience in each period a forward drift which decreases with greater depth.
We theoretically and numerically prove that under an electromagnetic plane wave with linear polarization incident normally to cylindrical passive scatterers, a single energy diagram can integrate absorption, scattering, and extinction cross…
In this paper we consider energy decay estimates for the Cauchy problems of dissipative wave equations with time dependent coefficients, in particular, the coefficients consisting of weak dissipation and very fast oscillating terms. For…
It is known that the asymptotic behavior of time-dependent dissipative coefficient in the Cauchy problem of dissipative wave equation dominates the energy decay estimate. In particular, it is important to study the case where the…
The hierarchy of integrable equations are considered. The dynamical approach to the theory of nonlinear waves is proposed. The special solutions(nonlinear waves) of considered equations are derived. We use powerful methods of computer…
We undertake a systematic review of some results concerning local well-posedness of the Cauchy problem for certain systems of nonlinear wave equations, with minimal regularity assumptions on the initial data. Moreover we provide a…
In this paper we derive some new weakly nonlinear asymptotic models describing viscous waves in deep water with or without surface tension effects. These asymptotic models take into account several different dissipative effects and are…
The main purpose of this expository note is to give a short account of the recent developments in mathematical wave kinetic theory. After reviewing the physical theory, we explain the importance of the notion of a scaling law, which…
We study a system of semilinear wave equations on Kerr backgrounds that satisfies the weak null condition. Under the assumption of small initial data, we prove global existence and pointwise decay estimates.
The zero angle scattered wave plays an essential role in the celebrated Optical Theorem that relates the total extinction cross section (including both scattering and absorption) to the complex amplitude of the scattered wave. In an…
The linearized water-wave radiation problem for an oscillating submerged line source in an inviscid shear flow with a free surface is investigated analytically at finite, constant depth in the presence of a shear flow varying linearly with…
Based on the analysis of 6.031*10^7 K+- --> pi0 pi0 pi+- decays, the NA48/2 collaboration has recently determined the S-wave pi-pi scattering lengths a_0-a_2 with high precision. In addition, the scattering length a_2 has been independently…
We consider Morawetz estimates for weighted energy decay of solutions to the wave equation on scattering manifolds (i.e., those with large conic ends). We show that a Morawetz estimate persists for solutions that are localized at low…
We study the stabilization and the wellposedness of solutions of the wave equation with subcritical semilinearities and locally distributed nonlinear dissipation. The novelty of this paper is that we deal with the difficulty that the main…
Encyclopedic article covering shallow water wave models used in oceanography and atmospheric science. Sections: Definition of the Subject; Introduction and Historical Perspective; Completely Integrable Shallow Water Wave Equations; Shallow…
The topographical scattering of gravity waves is investigated using a spectral energy balance equation that accounts for first order wave-bottom Bragg scattering. This model represents the bottom topography and surface waves with spectra,…
We prove a dispersive estimate for the solutions of the linearized Water-Waves equations in dimension 1 in presence of a flat bottom. We prove a decay with respect to time t of order 1/3 for solutions with initial data in weighted Sobolev…
We consider the initial-value problem for the one-dimensional, time-dependent wave equation with positive, Lipschitz continuous coefficients, which are constant outside a bounded region. Under the assumption of compact support of the…