Related papers: Symmetric hyperbolicity and consistent boundary co…
We introduce a class of singular partial differential equations, the second-order hyperbolic Fuchsian systems, and we investigate the associated initial value problem when data are imposed on the singularity. First of all, we analyze a…
We give a well posed initial value formulation of the Baumgarte-Shapiro-Shibata-Nakamura form of Einstein's equations with gauge conditions given by a Bona-Masso like slicing condition for the lapse and a frozen shift. This is achieved by…
We study the dynamics of Einstein's equations in Ashtekar's variables from the point of view of the theory of hyperbolic systems of evolution equations. We extend previous results and show that by a suitable modification of the Hamiltonian…
We prove the well--posedness of a dynamical perfect plasticity model under general assumptions on the stress constraint set and on the reference configuration. The problem is studied by combining both calculus of variations and hyperbolic…
We study asymptotically constrained systems for numerical integration of the Einstein equations, which are intended to be robust against perturbative errors for the free evolution of the initial data. First, we examine the previously…
We consider $n+1$ dimensional smooth Riemannian and Lorentzian spaces satisfying Einstein's equations. The base manifold is assumed to be smoothly foliated by a one-parameter family of hypersurfaces. In both cases---likewise it is usually…
In the first part of this work we show a uniqueness result for globally hyperbolic spacetimes with a spacelike conformal boundary satisfying the vacuum Einstein equations with positive cosmological constant. Then we present applications of…
In this paper, we initiate the study of the asymptotically AdS initial-boundary value problem for the Einstein-massless Vlasov system with $\Lambda<0$ in spherical symmetry. We will establish the existence and uniqueness of a maximal future…
This paper discusses the initial-boundary value problem (with a nonhomogeneous boundary condition) for a multi-dimensional scalar first-order conservation law with a multiplicative noise. One introduces a notion of kinetic formulations in…
We show that the 3+1 vacuum Einstein field equations in Ashtekar's variables constitutes a first order symmetric hyperbolic system for arbitrary but fixed lapse and shift fields, by suitable adding to the system terms proportional to the…
This article solves the initial boundary value problem for the vacuum Einstein equations with a negative cosmological constant in dimension 4, giving rise to asymptotically Anti-de Sitter spaces. We introduce a new family of geometric…
Second-order formulations of the 3+1 Einstein equations obtained by eliminating the extrinsic curvature in terms of the time derivative of the metric are examined with the aim of establishing whether they are well posed, in cases of…
We discuss a class of linear control problems in a Hilbert space setting, which covers diverse systems such as hyperbolic and parabolic equations with boundary control and boundary observation even including memory terms. We introduce…
In addition to the second-order Einstein equations on four-dimensional homogeneous isotropic background universe filled with the single perfect fluid, we also derived the second-order perturbations of the continuity equation and the Euler…
First-order hyperbolic systems are promising as a basis for numerical integration of Einstein's equations. In previous work, the lapse and shift have typically not been considered part of the hyperbolic system and have been prescribed…
In this manuscript, we put forth a general scheme for defining initial value problems from Einstein's equations of General Relativity constrained by homogeneous and isotropic expansion. The cosmological models arising as solutions are…
In this paper, we introduce the notion of boundary delay equations, establishing a unified framework for analyzing linear time-invariant systems with pure time-delayed boundary conditions. We establish mild sufficient conditions for the…
We analyze Einstein's vacuum field equations in generalized harmonic coordinates on a compact spatial domain with boundaries. We specify a class of boundary conditions which is constraint-preserving and sufficiently general to include…
In this work we study linear Maxwell equations with time- and space-dependent matrix-valued permittivity and permeability on domains with a perfectly conducting boundary. This leads to an initial boundary value problem for a first order…
We establish a variant, which has the advantage of introducing only physical characteristics, of the symmetric quasi linear first order system given by H.\ Friedrich for the evolution equations of gravitating fluid bodies in General…