Related papers: Cauchy-characteristic extraction in numerical rela…
A review of the treatment of boundaries in general relativity is presented with the emphasis on application to the formulations of Einstein's equations used in numerical relativity. At present, it is known how to treat boundaries in the…
Towards the investigation of the full dynamics in higher-dimensional and/or stringy gravitational model, we present the basic equations of the Einstein-Gauss-Bonnet gravity theory. We show $(N+1)$-dimensional version of the ADM…
We study the dynamics of a bounded gravitational collapsing configuration emitting gravitational waves, where the exterior spacetime is described by Robinson-Trautman geometries. The full nonlinear regime is examined by using the Galerkin…
We focus on eventually non-linear abstract Cauchy problems with a generalized fractional derivative in time. First we prove a local existence and uniqueness result, then we focus on a generalized Gr\"onwall inequality. Before addressing the…
This thesis is framed within the field of Mathematical Relativity and is organized into six chapters. After an introduction to the topic in Chapter 1, Chapter 2 reviews and further develops the formalism of hypersurface data, which provides…
We are developing 3 dimensional simulation codes for coalescing binary neutron stars. A code using the maximal slicing condition is obtained. To evaluate the gravitational radiation, we implemented a gauge-invariant wave extraction and…
We present a detailed methodology for extracting the full set of Newman-Penrose Weyl scalars from numerically generated spacetimes without requiring a tetrad that is completely orthonormal or perfectly aligned to the principal null…
We consider the Cauchy problem for stochastic fractional evolution equations with Caputo time fractional derivative of order $1<\alpha<2$ and space variable coefficients on an unbounded domain. The space derivatives that appear in the…
In this paper we consider the " exterior approach " to solve the inverse obstacle problem for the heat equation. This iterated approach is based on a quasi-reversibility method to compute the solution from the Cauchy data while a simple…
The characteristic formalism of numerical relativity is based on a system of coordinates aligned with outgoing null cones. While these coordinates were designed for studying gravitational waves, they can also be easily adapted to model…
We establish an optimal gluing construction for general relativistic initial data sets. The construction is optimal in two distinct ways. First, it applies to generic initial data sets and the required (generically satisfied) hypotheses are…
We develop a unified nonparametric framework for sharp partial identification and inference on inequality indices when the data contain coarsened observations of the variable of interest. We characterize the extremal allocations for all…
We consider inverse boundary value problems for elliptic equations of second order of determining coefficients by Dirichlet-to-Neumann map on subboundaries, that is, the mapping from Dirichlet data supported on $\partial\Omega\setminus…
We study a nonlinear initial value Cauchy problem depending upon a complex perturbation parameter $\epsilon$ with vanishing initial data at complex time $t=0$ and whose coefficients depend analytically on $(\epsilon,t)$ near the origin in…
Combining incoming and outgoing characteristic formulations can provide numerical relativists with a natural implementation of Einstein's equations that better exploits the causal properties of the spacetime and gives access to both null…
We consider gravitational field equations which are Einstein equations written in terms of embedding coordinates in some higher dimensional Minkowski space. Our main focus is to address some tricky issues relating to the Cauchy problem and…
We consider the Cauchy problem for the equations of pressureless gases in two space dimensions. For a generic set of smooth initial data (density and velocity), it is known that the solution loses regularity at a finite time $t_0$, where…
We consider the Cauchy problem for doubly non-linear degenerate parabolic equations on Riemannian manifolds of infinite volume, or in $\R^N$. The equation contains a weight function as a capacitary coefficient which we assume to decay at…
In this paper, we study the Cauchy problem for the Riccati differential equation with constant coefficients and a modified Gerasimov-Caputo type fractional differential operator of variable order. Using Newton's numerical algorithm,…
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…