Related papers: Cauchy-perturbative matching and outer boundary co…
A problem of a wave identification is formulated. An example is considered in conditions of one-dimensional Cauchy problem for conventional string equation in matrix form and its inhomogeneous two-component version. The acoustic and…
Computational methods are essential to provide waveforms from coalescing black holes, which are expected to produce strong signals for the gravitational wave observatories being developed. Although partial simulations of the coalescence…
Solving Einstein's equations precisely for strong-field gravitational systems is essential to determining the full physics content of gravitational wave detections. Without these solutions it is not possible to infer precise values for…
We present a new formulation of the multipolar expansion of an exact boundary condition for the wave equation, which is truncated at the quadrupolar order. Using an auxiliary function, that is the solution of a wave equation on the sphere…
Stable computational algorithms for the approximate solution of the Cauchy problem for nonstationary problems are based on implicit time approximations. Computational costs for boundary value problems for systems of coupled multidimensional…
We consider a series of distorted black hole initial data sets, and develop techniques to evolve them using the linearized equations of motion for the gravitational wave perturbations on a Schwarzschild background. We apply this to 2D and…
We present an implementation of absorbing boundary conditions for the Einstein equations based on the recent work of Buchman and Sarbach. In this paper, we assume that spacetime may be linearized about Minkowski space close to the outer…
We study neural field equations, which are prototypical models of large-scale cortical activity, subject to random data. We view this spatially-extended, nonlocal evolution equation as a Cauchy problem on abstract Banach spaces, with…
This paper sets up a perturbative treatment of the evolving quantum state of a gravitational system, in a Schr\"odinger-like picture, working about a general background. This connects gauge symmetry, the constraints, gravitational dressing,…
We incorporate a massless scalar field into a 3-dimensional code for the characteristic evolution of the gravitational field. The extended 3-dimensional code for the Einstein--Klein--Gordon system is calibrated to be second order…
Gravitational wave background results from the superposition of gravitational waves generated from all sources across the Universe. Previous efforts on detecting such a background with pulsar timing arrays assume it is an isotropic Gaussian…
In this paper, the regularity properties of Cauchy problem for linear and nonlinear nonlocal wave equations are studied.The equation involves a convolution integral operators with a general kernel operator functions whose Fourier transform…
We study non-linear evolution equations with periodic initial conditions. In particular, we use the graph method introduced by Galavotti to prove the existence of global solution of Hamiltonian perturbation of KdV without any restriction on…
Binary black hole interactions provide potentially the strongest source of gravitational radiation for detectors currently under development. We present some results from the Binary Black Hole Grand Challenge Alliance three- dimensional…
In a recent article, we constructed a hierarchy B_L of outer boundary conditions for Einstein's field equations with the property that, for a spherical outer boundary, it is perfectly absorbing for linearized gravitational radiation up to a…
The extraction of the gravitational wave signal, within the context of a characteristic numerical evolution is revisited. A formula for the gravitational wave strain is developed and tested, and is made publicly available as part of the…
I discuss the conformal approach to the numerical simulation of radiating isolated systems in general relativity. The method is based on conformal compactification and a reformulation of the Einstein equations in terms of rescaled…
We consider the Cauchy problem for coupled systems of wave and Klein-Gordon equations with quadratic nonlinearity in three space dimensions. We show global existence of small amplitude solutions under certain condition including the null…
We study linear damped and viscoelastic wave equations evolving on a bounded domain. For both models, we assume that waves are subject to an inhomogeneous Neumann boundary condition on a portion of the domain's boundary. The analysis of…
In this paper, we discuss the Cauchy Problem for the compressible isentropic Euler-Boltzmann equations with vacuum in radiation hydrodynamics. Firstly, we establish the local existence of regular solutions by the fundamental methods in the…