相关论文: On the AdS stability problem

We consider the stability in the inverse problem consisting of the determination of a time-dependent coefficient of order zero $q$, appearing in a Dirichlet initial-boundary value problem for a wave equation $\partial_t^2u-\Delta…

We study a semilinear differential-algebraic equation (DAE) with the focus on the Lagrange stability (instability). The conditions for the existence and uniqueness of global solutions (a solution exists on an infinite interval) of the…

We consider the $L^2$-boundedness of the solution itself of the Cauchy problem for wave equations with time-dependent wave speeds. We treat it in the one-dimensional Euclidean space. To study these, we adopt a simple multiplier method by…

Algorithmic stability is a central concept in statistics and learning theory that measures how sensitive an algorithm's output is to small changes in the training data. Stability plays a crucial role in understanding generalization,…

We consider spherically symmetric Einstein-massless-scalar field equations with negative cosmological constant in five dimensions and analyze evolution of small perturbations of anti-de Sitter spacetime using the recently proposed resonant…

Computational techniques which establish the stability of an evolution-boundary algorithm for a model wave equation with shift are incorporated into a well-posed version of the initial-boundary value problem for gravitational theory in…

The 2-sets convex feasibility problem aims at finding a point in the intersection of two closed convex sets $A$ and $B$ in a normed space $X$. More generally, we can consider the problem of finding (if possible) two points in $A$ and $B$,…

The existence of adversarial examples has led to considerable uncertainty regarding the trust one can justifiably put in predictions produced by automated systems. This uncertainty has, in turn, lead to considerable research effort in…

The question of stability of steady spherical accretion has been studied for many years and, recently, the concept of spatial instability has been introduced. Here we study perturbations of steady spherical accretion flows (Bondi…

Cosmological boundary conditions for particles and fields are often discussed as a Cauchy problem, in which configurations and conjugate momenta are specified on an "initial" time slice. But this is not the only way to specify boundary…

We consider the stability of the toroidal AdS-Schwarzshild black holes as solutions of the Einstein--Klein-Gordon system, with Dirichlet or Neumann boundary conditions for the scalar field. Restricting to perturbations that respect the…

Since the solution of the so-called folk problems of smoothability, there has been a special interest in the properties of classical time and volume functions of spacetimes. Here we supply some information that complements the one provided…

Weakly nonlinear dynamics in anti-de Sitter (AdS) spacetimes is reviewed, keeping an eye on the AdS instability conjecture and focusing on the resonant approximation that accurately captures in a simplified form the long-term evolution of…

New approaches to the study of stability of solutions of Set Differential Equations (SDEs) based on convex geometry and the theory of mixed volumes were proposed. The stability of the forms of program solutions of linear SDEs with a stable…

The paper is concerned with sticky weak solutions to the equations of pressureless gases in two or more space dimensions. Various initial data are constructed, showing that the Cauchy problem can have (i) two distinct sticky solutions, or…

In general relativity, perturbation theory about a background solution fails if the background spacetime has a Killing symmetry and a compact spacelike Cauchy surface. This failure, dubbed as {\it linearization instability}, shows itself as…

We consider a class of nonlinear Schroedinger equation in three space dimensions with an attractive potential. The nonlinearity is local but rather general encompassing for the first time both subcritical and supercritical (in $L^2$)…

In [1], the authors have studied stability of certain causal properties of space-times in general relativity. As a continuation of this work, in the present paper, we review and discuss, some more aspects of stability which occur in various…

This paper continues the studies of symbolic integration by focusing on the stability problems on D-finite functions. We introduce the notion of stability index in order to investigate the order growth of the differential operators…

The determination of the stability of the long-lived consensus problem is a fundamental open problem in distributed systems. We concentrate on the memoryless binary case with geodesic paths. We offer a conjecture on the stability in this…