Related papers: Wave Propagation and Scattering for the RS2 Brane …
This paper is devoted to the proof of a global existence result for the water waves equation with smooth, small, and decaying at infinity Cauchy data. We obtain moreover an asymptotic description in physical coordinates of the solution,…
Consider the Cauchy problem for the radial cubic wave equation in 1+3 dimensions with either the focusing or defocusing sign. This problem is critical in $\dot{H}^{\frac{1}{2}} \times \dot{H}^{-\frac{1}{2}}$ and subcritical with respect to…
The present work investigates some exact solutions of the gravitational wave equation in some widely used cosmological spacetimes. The examples are taken from spatially flat and closed isotropic models as well as Kasner metric which is…
We obtain a solution describing a gravitational shockwave propagating along a Randall-Sundrum brane. The interest of such a solution is twofold: on the one hand, it is the first exact solution for a localized source on a Randall-Sundrum…
We investigate scattering properties of a Moyal deformed version of the nonlinear Schr\"odinger equation in an even number of space dimensions. With rather weak conditions on the degree of nonlinearity, the Cauchy problem for general…
We consider wave equations on Lorentzian manifolds in case of low regularity. We first extend the classical solution theory to prove global unique solvability of the Cauchy problem for distributional data and right hand side on smooth…
In this paper, we investigate gravitational waves as metric perturbations around a general warped 5-dimensional background. We find an analytical solution in Randall-Sundrum braneworld model and analyze the implications of braneworld models…
In this paper, we establish a conformal scattering theory for defocusing semilinear wave equations on Schwarzschild spacetime. We combine the energy and pointwise decay results for solutions obtained in \cite{Yang} with a Sobolev embedding…
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…
The causal structure of the flat brane universe of RSII type is re-investigated to clarify the boundary conditions for stochastic gravitational waves. In terms of the Gaussian normal coordinate of the brane, a singularity of the equation…
We consider the Cauchy problem with smooth and compactly supported initial data for the wave equation in a general class of spherically symmetric geometries which are globally smooth and asymptotically flat. Under certain mild conditions on…
We consider the Cauchy problem of the gravitational wave with the initial data distributed only around the brane in the one brane model of Randall and Sundrum, and examine its behavior as t\to\infty. Then we find its leading behavior is…
We investigate the Cauchy problem for a 2x2-system of weakly coupled semi-linear fractional wave equations with polynomial nonlinearities posed in R+ x RN. Under appropriate conditions on the exponents and the fractional orders of the time…
We numerically evolve spherically symmetric solutions to the linear wave equation on some expanding Friedmann-Lema\^itre-Robertson-Walker (FLRW) spacetimes and study the respective asymptotics for large times. We find a quantitative…
We study gravitational waves in the black string Randall-Sundrum braneworld. We present a reasonably self-contained and complete derivation of the equations governing the evolution of gravitational perturbations in the presence of a brane…
We carefully investigate the gravitational perturbation of the Randall-Sundrum (RS) single brane-world solution [hep-th/9906064], based on a covariant curvature tensor formalism recently developed by us. Using this curvature formalism, it…
We study both of the scattering and Cauchy problems for the semilinear wave equation with null quadratic form on the Schwarzschild background. Prescribing the scattering data that are given by the short pulse data on the future null…
Motivated by the problem of the evolution of bulk gravitational waves in Randall-Sundrum cosmology, we develop a characteristic numerical scheme to solve 1+1 dimensional wave equations in the presence of a moving timelike boundary. The…
The Cauchy problem is considered for the scalar wave equation in the Schwarzschild geometry. Using an integral spectral representation we derive the exact decay rate for solutions of the Cauchy problem with spherical symmetric initial data,…
Motivated by the strong cosmic censorship conjecture, we study the linear scalar wave equation in the interior of subextremal strictly charged Reissner-Nordstr\"om black holes by analyzing a suitably-defined "scattering map" at $0$…