Related papers: Hyers-Ulam stability for finite-dimensional nonaut…
This paper aims at studying a generalized Camassa--Holm equation under random perturbation. We establish a local well-posedness result in the sense of Hadamard, i.e., existence, uniqueness and continuous dependence on initial data, as well…
In this paper, we consider the stability of the Lamb dipole solution of the two-dimensional Euler equations in $\mathbb{R}^{2}$ and question under which initial disturbance the Lamb dipole is stable, motivated by experimental work on the…
Necessary and sufficient conditions for the internal stability of formations whose dynamics are obtained is determined by linear differential equations.
This paper proposes a framework to assess the stability of an ordinary differential equation which is coupled to a 1D-partial differential equation (PDE). The stability theorem is based on a new result on Integral Quadratic Constraints…
The purpose of this paper is to summarize the recent results on the stability of the parametric fundamental equation of information. Furthermore, by the help of a modification of a method we used in \cite{GM08} we shall give a unified proof…
We prove new characterisations of exponential stability for positive linear discrete-time systems in ordered Banach spaces, in terms of small-gain conditions. Such conditions have played an important role in the finite-dimensional systems…
We prove that for a wide family of non-uniformly hyperbolic maps and hyperbolic potentials we have equilibrium stability, i.e. the equilibrium states depend continuously on the dynamics and the potential. For this we deduce that the…
This paper studies inf-sup stable finite element discretizations of the evolutionary Navier--Stokes equations with a grad-div type stabilization. The analysis covers both the case in which the solution is assumed to be smooth and…
Higher-order time integration methods that unconditionally preserve the positivity and linear invariants of the underlying differential equation system cannot belong to the class of general linear methods. This poses a major challenge for…
The aim of this paper is to investigate the response of this system/scheme in terms of stability in presence of explicitly treated residual terms, as it inevitably occurs in the reality of NWP. This sudy is restricted to the impact of…
Stability and stabilization of linear port-Hamiltonian systems on infinite-dimensional spaces are investigated. This class is general enough to include models of beams and waves as well as transport and Schr\"odinger equations with boundary…
In this paper, we present sufficient conditions for asymptotic stability and exponential stability of a class of impulsive neutral differential equations with discrete and distributed delays. Our approaches are based on the method using…
This papers shows that nonlinear filter in the case of deterministic dynamics is stable with respect to the initial conditions under the conditions that observations are sufficiently rich, both in the context of continuous and discrete time…
The main purpose of this paper is to formulate new conditions for smooth linearization of nonautonomous systems with discrete and continuous time. Our results assume that the linear part admits a very general form of dichotomy known as…
The generalized Hyers--Ulam--Rassias stability of generalized derivations on unital Banach algebras into Banach bimodules is established.
The paper deals with the problem of existence of a convergent "strong" normal form in the neighbourhood of an equilibrium, for a finite dimensional system of differential equations with analytic and time-dependent non-linear term. The…
In this work, we study continuity and topological structural stability of attractors for nonautonomous random differential equations obtained by small bounded random perturbations of autonomous semilinear problems. First, we study existence…
Non-conservative loads of the follower type are usually believed to be the source of dynamic instabilities such as flutter and divergence. It is shown that these instabilities (including Hopf bifurcation, flutter, divergence, and…
In this paper, the existence conditions of nonuniform mean-square exponential dichotomy (NMS-ED) for a linear stochastic differential equation (SDE) are established. The difference of the conditions for the existence of a nonuniform…
We design observer-based controllers to stabilise abstract linear boundary control systems on Hilbert spaces. Our main results introduce conditions for exponential, strong, and polynomial stability, and establish external well-posedness of…