Related papers: Cauchy-characteristic extraction in numerical rela…
We consider gravitational radiation in the presence of non-compact extra dimensions. If their number is odd, all spacetime becomes odd-dimensional and formation of gravitational radiation becomes non-trivial because of violation of the…
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…
We consider the Hamiltonian dynamics of spherically symmetric Einstein gravity with a thin null-dust shell, under boundary conditions that fix the evolution of the spatial hypersurfaces at the two asymptotically flat infinities of a…
We consider the defocusing nonlinear wave equation of power-type on $\mathbb{R}^3$. We establish an almost sure global existence result with respect to a suitable randomization of the initial data. In particular, this provides examples of…
The inhomogenous time-fractional telegraph equation with Caputo derevatives with constant coefficients is considered. For considered equation the general representation of regular solution in rectangular domain is obtained, and the…
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…
In this paper, we give a criterion on the Cauchy data for the semilinear wave equations satisfying the null condition in $\mathbb{R}^+\times\mathbb{R}^{3}$ such that the energy of the data can be arbitrarily large while the solution is…
We present convergent gravitational waveforms extracted from three-dimensional, numerical simulations in the wave zone and with causally disconnected boundaries. These waveforms last for multiple periods and are very accurate, showing a…
We consider a system of nonlinear wave equations with constraints that arises from the Einstein equations of general relativity and describes the geometry of the so-called Gowdy symmetric spacetimes on T3. We introduce two numerical…
We carry out a study of the exterior of an axially and reflection symmetric source of gravitational radiation. The exterior of such a source is filled with a null fluid produced by the dissipative processes inherent to the emission of…
We consider a class of wave-Schroedinger systems with a Zakharov-Schulman type coupling. This class of systems is indexed by a parameter gamma which measures the strength of the null form in the nonlinearity of the wave equation. The case…
In the past we have considered Gaussian random matrix ensembles in the presence of an external matrix source. The reason was that it allowed, through an appropriate tuning of the eigenvalues of the source, to obtain results on non-trivial…
In this work we investigate Cauchy problem and initial boundary value problem for time-fractional Airy equation on the graphs with infinite and finite bonds. We studied properties of potentials for this equation and using these properties…
The aim of this article is to propose a systematic study of transparent boundary conditions for finite difference approximations of evolution equations. We try to keep the discussion at the highest level of generality in order to apply the…
We address the generation of initial conditions (ICs) for GRAMSES, a code for nonlinear general relativistic (GR) $N$-body cosmological simulations recently introduced in Ref. [1]. GRAMSES adopts a constant mean curvature slicing with a…
A non-Gaussian Hardy equation is studied with a non-linearity of Osgood-type growth. A fractional derivative in time is incorporated for the first time in an research of this type. Existence of local and global solutions are established by…
In this work a new numerical technique to prepare Cauchy data for the initial value problem (IVP) formulation of Einstein's field equations is presented. Directly inspired by the exterior asymptotic gluing (EAG) result of Corvino (2000) our…
We study the following problem: Given initial data on a compact Cauchy horizon, does there exist a unique solution to wave equations on the globally hyperbolic region? Our main results apply to any spacetime satisfying the null energy…
A study is presented for the non linear evolution of a self gravitating distribution of matter coupled to a massless scalar field. The characteristic formulation for numerical relativity is used to follow the evolution by a sequence of…
We prove global pointwise decay estimates for a class of defocusing semilinear wave equations in $n=3$ dimensions restricted to spherical symmetry. The technique is based on a conformal transformation and a suitable choice of the mapping…