相关论文: Spijker's example and its extension

We study the stability of solution branches for the Lichnerowicz-York equation at moment of time symmetry with constant unscaled energy density. We prove that the weak-field lower branch of solutions is stable whilst the upper branch of…

A framework for the analysis of stochastic models of chemical systems for which the deterministic mean-field description is undergoing a saddle-node infinite period (SNIPER) bifurcation is presented. Such a bifurcation occurs for example in…

The paper addresses stability and finite element analysis of the stationary two-phase Stokes problem with a piecewise constant viscosity coefficient experiencing a jump across the interface between two fluid phases. We first prove a priori…

We consider viscous two-dimensional steady flows of incompressible fluids past doubly periodic arrays of solid obstacles. In a class of such flows, the autocorrelations for the Lagrangian observables decay in accordance with the power law,…

Linear systems governed by continuous-time difference equations cover a wide class of linear systems. From the Lyapunov-Krasovskii approach, we investigate stability for such a class of systems. Sufficient conditions, and in some particular…

Linear stability of both sign-definite (positive) and sign-indefinite solitary waves near pitchfork bifurcations is analyzed for the generalized nonlinear Schroedinger equations with arbitrary forms of nonlinearity and external potentials…

We propose a theoretical approach to derive amplitude equations governing the weakly nonlinear evolution of nonnormal dynamical systems when they experience transient growth or respond to harmonic forcing. This approach reconciles the…

In a posteriori error analysis, the relationship between error and estimator is usually spoiled by so-called oscillation terms, which cannot be bounded by the error. In order to remedy, we devise a new approach where the oscillation has the…

It is a well-known rule of thumb that approximations of stochastic partial differential equations have essentially twice the order of weak convergence compared to the corresponding order of strong convergence. This is already known for many…

Fractional difference equations provide a flexible mathematical framework for modeling complex systems with memory, hereditary, and non-local effects. In this work, we study the stability of higher-order two-term fractional linear…

We show that bimodal systems with a spatially nonuniform defocusing cubic nonlinearity, whose strength grows toward the periphery, can support stable two-component solitons. For a sufficiently strong XPM interaction, vector solitons with…

We present a theoretical analysis of stochastic optimization methods in terms of their sensitivity with respect to the step size. We identify a key quantity that, for each method, describes how the performance degrades as the step size…

We study the question of weak solvability for a nonlinear coupled parabolic system that models the evolution of a complex pedestrian flow. The main feature is that the flow is composed of a mix of densities of active and passive pedestrians…

In this paper, we study the existence and uniqueness of weak solution of a nonlinear poroelasticity model. To better describe the proccess of deformation and diffusion underlying in the original model, we firstly reformulate the nonlinear…

Using a {\it collective} Monte Carlo algorithm we study the low-temperature and long-distance properties of two systems of two-dimensional classical tops. Both systems have the same spin-wave dynamics (low-temperature behavior) as a large…

We study $\varepsilon$-stability in continuous logic. We first consider stability in a model, where we obtain a definability of types result with a better approximation than that in the literature. We also prove forking symmetry for…

We give an example of a symplectic manifold with a stable hypersurface such that nearby hypersurfaces are typically unstable.

The stable-regenerative multiple-stable model has been shown recently to have distinct candidate extremal index and extremal index. To understand further this rare phenomenon, two more results are established here for the double-stable…

By large scale Monte Carlo simulations it is shown that the stable fixed point of the SO(5) theory is either bicritical or tetracritical depending on the effective interaction between the antiferromagnetism and superconductivity orders.…

Due to the existence of multiple stationary distributions, we study the stability and instability of a stationary distribution for distribution dependent stochastic differential equations. This note is devoted to the instability of a…