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Super-stability and strong stability are properties of a matching in the stable matching problem with ties. In this paper, we introduce a common generalization of super-stability and strong stability, which we call non-uniform stability.…
The paper is focused on the nonlinear stability analysis of stochastic $\theta$-methods. In particular, we consider nonlinear stochastic differential equations such that the mean-square deviation between two solutions exponentially decays,…
The emergent mechanism provides a possible way to resolve the big bang singularity problem by assuming that our universe originates from the Einstein static (ES) state. Thus, the existence of a stable ES solution becomes a very crucial…
We study the positive, regular, radially symmetric solutions to the nonlinear biharmonic equation $\Delta^2 \phi = \phi^p$. First, we show that there exists a critical value $p_c$, depending on the space dimension, such that the solutions…
We consider the incompressible Euler equations in $R^2$ when the initial vorticity is bounded, radially symmetric and non-increasing in the radial direction. Such a radial distribution is stationary, and we show that the monotonicity…
We analyze the spectral stability of small-amplitude, periodic, traveling-wave solutions of the Kawahara equation. These solutions exhibit high-frequency instabilities when subject to bounded perturbations on the whole real line. We…
Linear stability of stratified two-phase flows in horizontal channels to arbitrary wavenumber disturbances is studied. The problem is reduced to Orr-Sommerfeld equations for the stream function disturbances, defined in each sublayer and…
This is the second paper in a series studying the nonlinear stability of rarefaction waves in multi-dimensional gas dynamics. We construct initial data near singularities in the rarefaction wave region and, combined with the a priori energy…
The linear stability of stratified two-phase flows in rectangular ducts is studied numerically. The linear stability analysis takes into account all possible infinitesimal three-dimensional disturbances and is carried out by solution of the…
This paper deals with stability of discrete-time switched linear systems whose all subsystems are unstable. We present sufficient conditions on the subsystems matrices such that a switched system is globally exponentially stable under a set…
In this paper we characterise the global stability, global boundedness and recurrence of solutions of a scalar nonlinear stochastic differential equation. The differential equation is a perturbed version of a globally stable autonomous…
This paper considers robust stability analysis of a large network of interconnected uncertain systems. To avoid analyzing the entire network as a single large, lumped system, we model the network interconnections with integral quadratic…
This paper concerns a question that frequently occurs in various applications: Is any diffusive coupling of stable linear systems, also stable? Although it has been known for a long time that this is not the case, we shall identify a…
In this paper, we study the polynomial stability of analytical solution and convergence of the semi-implicit Euler method for non-linear stochastic pantograph differential equations. Firstly, the sufficient conditions for solutions to grow…
We survey the numerical stability of some fast algorithms for solving systems of linear equations and linear least squares problems with a low displacement-rank structure. For example, the matrices involved may be Toeplitz or Hankel. We…
Following Smale, we study simple symmetric mechanical systems of $n$ point particles in the plane. In particular, we address the question of the linear and spectral stability properties of relative equilibria, which are special solutions of…
The aim of this Note is to prove by a perturbation method the existence of solutions of the coupled Einstein-Dirac-Maxwell equations for a static, spherically symmetric system of two fermions in a singlet spinor state and with the…
We apply analytical and numerical methods to study the linear stability of stripe patterns in two generalizations of the two-dimensional Swift-Hohenberg equation that include coupling to a mean flow. A projection operator is included in our…
In this paper we consider the global stability of solutions of a nonlinear stochastic differential equation. The differential equation is a perturbed version of a globally stable linear autonomous equation with unique zero equilibrium where…
In this paper, we study stability properties of nonuniform hyperbolicity for evolution processes associated with differential equations in Banach spaces. We prove a robustness result of nonuniform hyperbolicity for linear evolution…