Related papers: Boundary conditions for Einstein's field equations…
The dynamics of quantum field theories on bounded domains requires the introduction of boundary conditions on the quantum fields. We address the problem from a very general perspective by using charge conservation as a fundamental principle…
We study and develop constraint preserving boundary conditions for the Newtonian magnetohydrodynamic equations and analyze the behavior of the numerical solution upon considering different possible options.
In this paper we obtain natural boundary conditions for a large class of variational problems with free boundary values. In comparison with the already existing examples, our framework displays complete freedom concerning the topology of…
We make use of the metric version of the conformal Einstein field equations to construct anti-de Sitter-like spacetimes by means of a suitably posed initial-boundary value problem. The evolution system associated to this initial-boundary…
Excision techniques are used in order to deal with black holes in numerical simulations of Einstein equations and consist in removing a topological sphere containing the physical singularity from the numerical domain, applying instead…
This paper is concerned with the initial-boundary value problem for a nonlinear hyperbolic system of conservation laws. We study the boundary layers that may arise in approximations of entropy discontinuous solutions. We consider both the…
We present a set of effective outflow/open boundary conditions and an associated algorithm for simulating the dynamics of multiphase flows consisting of $N$ ($N\geqslant 2$) immiscible incompressible fluids in domains involving outflows or…
In this paper, we propose two approaches to apply boundary conditions for bond-based peridynamic models. There has been in recent years a renewed interest in the class of so-called non-local models, which include peridynamic models, for the…
We analyse dissipative boundary conditions for nonlinear hyperbolic systems in one space dimension. We show that a previous known sufficient condition for exponential stability with respect to the C^1-norm is optimal. In particular a known…
In this paper we study a numerical implementation for the initial boundary value formulation for the generalized conformal field equations. We propose a formulation which is well suited for the study of the long-time behaviour of perturbed…
The generalized harmonic representation of Einstein's equation is manifestly hyperbolic for a large class of gauge conditions. Unfortunately most of the useful gauges developed over the past several decades by the numerical relativity…
We study boundary conditions for the bosonic, spinning (NSR) and Green-Schwarz open string, as well as for 1+1 dimensional supergravity. We consider boundary conditions that arise from (1) extremizing the action, (2) BRST, rigid or local…
Using holographic-fluid techniques, we discuss some aspects of the integrability properties of Einstein's equations in asymptotically anti-de Sitter spacetimes. We review and we amend the results of 1506.04813 on how exact four-dimensional…
We discuss the initial-boundary value problem of General Relativity. Previous considerations for a toy model problem in electrodynamics motivate the introduction of a variational principle for the lapse with several attractive properties.…
We numerically investigate the propagation of plane gravitational waves in the form of an initial boundary value problem with de Sitter initial data. The full non-linear Einstein equations with positive cosmological constant $\lambda$ are…
We linearize the Einstein equations when the metric is Bondi-Sachs, when the background is Schwarzschild or Minkowski, and when there is a matter source in the form of a thin shell whose density varies with time and angular position. By…
In this paper an exact transparent boundary condition (TBC) for the multidimensional Schr\"odinger equation in a hyperrectangular computational domain is proposed. It is derived as a generalization of exact transparent boundary conditions…
Invariance principles determine many key properties in quantum field theory, including, in particular, the appropriate form of the boundary conditions. A crucial consistency check is the proof that the resulting boundary-value problem is…
We show that the energy of classical solutions to the wave equation with hyperbolic boundary condition (i.e., dynamic Wentzell boundary condition) and damping on the boundary decays like 1/t. In fact we allow mixed boundary conditions: a…
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…