English
Related papers

Related papers: Stability problem of equilibrium discrete planar c…

200 papers

We are concerned with the Calder\'on problem of determining an unknown conductivity of a body from the associated boundary measurement. We establish a logarithmic type stability estimate in terms of the Hausdorff distance in determining the…

Analysis of PDEs · Mathematics 2019-02-13 Hongyu Liu , Chun-Hsiang Tsou

The diffusive viscous wave equation describes wave propagation in diffusive and viscous media. Examples include seismic waves traveling through the Earth's crust, taking into account of both the elastic properties of rocks and the…

Numerical Analysis · Mathematics 2025-01-13 Siyang Wang

We consider spherically symmetric spacetimes sourced by a fluid with pressure anisotropy in the radial direction. We use gauge-invariant perturbation theory to study the stability of this class of spacetimes under axial perturbations. We…

General Relativity and Quantum Cosmology · Physics 2014-07-23 Bhavesh Khamesra , V Suneeta

We consider the 2D Euler equation of incompressible fluids on a strip and prove the stability of the rectangular stationary state.

Analysis of PDEs · Mathematics 2016-11-08 J. Beichman , S. Denisov

In this article, we study the behavior of the stability of pullback of a vector bundle under a finite morphism from a (not necessarily smooth) stacky curve to an orbifold curve. We establish a categorical equivalence between proper formal…

Algebraic Geometry · Mathematics 2022-11-07 Soumyadip Das , Snehajit Misra

The stability of the bright solitary wave solution to the perturbed cubic-quintic Schroedinger equation is considered. It is shown that in a certain region of parameter space these solutions are unstable, with the instability being…

patt-sol · Physics 2009-10-30 Todd Kapitula

This paper investigates the stability of traveling wave solutions to the free boundary Euler equations with a submerged point vortex. We prove that sufficiently small-amplitude waves with small enough vortex strength are conditionally…

Analysis of PDEs · Mathematics 2019-07-30 Kristoffer Varholm , Erik Wahlén , Samuel Walsh

Many modern datasets don't fit neatly into $n \times p$ matrices, but most techniques for measuring statistical stability expect rectangular data. We study methods for stability assessment on non-rectangular data, using statistical learning…

Computation · Statistics 2021-02-23 Kris Sankaran

We first give a complete linearized stability analysis around stationary solutions of the Mullins-Sekerka flow with $90^\circ$ contact angle in two space dimensions. The stationary solutions include flat interfaces, as well as arcs of…

Analysis of PDEs · Mathematics 2019-07-02 Harald Garcke , Maximilian Rauchecker

In this article we discuss the role of stability functions in geometric invariant theory and apply stability function techniques to problems in toric geometry. In particular we show how one can use these techniques to recover results of…

Symplectic Geometry · Mathematics 2009-07-03 Daniel Burns , Victor Guillemin , Zuoqin Wang

Given a functional for a one-dimensional physical system, a classical problem is to minimize it by finding stationary solutions and then checking the positive definiteness of the second variation. Establishing the positive definiteness is,…

Classical Analysis and ODEs · Mathematics 2017-04-26 Thomas Lessinnes , Alain Goriely

We analyze the stability of generic spherically symmetric thin shells to linearized perturbations around static solutions. We include the momentum flux term in the conservation identity, deduced from the ''ADM'' constraint and the Lanczos…

General Relativity and Quantum Cosmology · Physics 2009-11-11 Francisco S. N. Lobo , Paulo Crawford

In this paper, we consider a non-linear fourth-order evolution equation of Cahn-Hilliard-type on evolving surfaces with prescribed velocity, where the non-linear terms are only assumed to have locally Lipschitz derivatives. High-order…

Numerical Analysis · Mathematics 2022-03-07 Cedric Aaron Beschle , Balázs Kovács

We study a generalized functional related to the pullback metrics (3). We derive the first variation formula which yield stationary maps. We introduce the stress-energy tensor which is naturally linked to conservation law and yield…

Differential Geometry · Mathematics 2017-07-11 Said Asserda

We study stationary solutions in the differential kinetic equation, which was introduced in for description of a local dual cascade wave turbulence. We give a full classification of single-cascade states in which there is a finite flux of…

Fluid Dynamics · Physics 2020-03-11 V. N. Grebenev , S. B. Medvedev , S. V. Nazarenko , B. V. Semisalov

In this paper we study the long time dynamics of the solutions to the initial-boundary value problem for a scalar conservation law with a saturating nonlinear diffusion. After discussing the existence of a unique stationary solution and its…

Analysis of PDEs · Mathematics 2024-05-21 Raffaele Folino , Maurizio Garrione , Marta Strani

In this paper, we study the probabilistic stability analysis of a subclass of stochastic hybrid systems, called the Planar Probabilistic Piecewise Constant Derivative Systems (Planar PPCD), where the continuous dynamics is deterministic,…

Robotics · Computer Science 2022-09-07 Spandan Das , Pavithra Prabhakar

We propose and analyze stable finite element approximations for Willmore flow of planar curves. The presented schemes are based on a novel weak formulation which combines an evolution equation for curvature with the curvature formulation…

Numerical Analysis · Mathematics 2025-09-29 Harald Garcke , Robert Nürnberg , Quan Zhao

In this paper the stability of the Korteweg-de Vries (KdV) equation is investigated. It is shown analytically and numerically that small perturbations of solutions of the KdV-equation introduce effects of dispersion, hence the perturbation…

solv-int · Physics 2008-02-03 H. J. S. Dorren , R. K. Snieder

We establish the Hyers-Ulam stability of certain linear first-order differential equations with singularities. We then extend these results to higher-order singular linear differential equations that can be written with these first-order…

Classical Analysis and ODEs · Mathematics 2013-08-01 Douglas R. Anderson , Jenna M. Otto