Related papers: Exponential stability of abstract evolution equati…
We study the asymptotic behaviour of the wave equation with viscoelastic damping in presence of a time-delayed damping. We prove exponential stability if the amplitude of the time delay term is small enough.
In our manuscript, we develop a new approach for stability analysis of one-dimensional wave equation with time delay. The major contribution of our work is to develop a new method for spectral analysis. We derive sufficient and necessary…
In this paper, we introduce the notion of boundary delay equations, establishing a unified framework for analyzing linear time-invariant systems with pure time-delayed boundary conditions. We establish mild sufficient conditions for the…
In this paper we analyze a nonlinear abstract evolution equation with an infinite number of time-dependent time delays and a Lipschitz continuous nonlinear term. By using a fixed point argument we prove the existence of a mild solution.…
In this paper we study time semi-discrete approximations of a class of exponentially stable infinite dimensional systems with unbounded feedbacks. It has recently been proved that for time semi-discrete systems, due to high frequency…
This paper deals with the stability of linear periodic difference delay systems, where the value at time $t$ of a solution is a linear combination with periodic coefficients of its values at finitely many delayed instants…
This paper explores the exponential stability of two nonlinear wave equations coupled through their velocities. The analysis is divided into two main cases. First, we consider a system where one equation is damped, while the other…
We study delay-independent stability in nonlinear models with a distributed delay which have a positive equilibrium. Such models frequently occur in population dynamics and other applications. In particular, we construct a relevant…
We study the question of existence of positive steady states of nonlinear evolution equations. We recast the steady state equation in the form of eigenvalue problems for a parametrised family of unbounded linear operators, which are…
Linear scalar differential equations with distributed delays appear in the study of the local stability of nonlinear differential equations with feedback, which are common in biology and physics. Negative feedback loops tend to promote…
In the present paper, the exponential stability of the mono-tubular heat exchanger equation with boundary observation possessing a time delay and inner control is investigated through a simply proportional feedback. Firstly, the close-loop…
For ordinary differential equations and functional differential equations the following result is well known. Suppose any solution is bounded on the half-line for each bounded on the half-line right-hand side. Then under certain conditions…
This paper is concerned with exponential stability of a class of infinite dimensional coupled systems. It is proved that under some admissibility conditions, the considered infinite dimensional coupled system is governed by a…
We provide explicit conditions for uniform stability, global asymptotic stability and uniform exponential stability for dynamic equations with a single delay and a nonnegative coefficient. Some examples on nonstandard time scales are also…
We show how strongly continuous semigroups can be associated with evolutionary equations. For doing so, we need to define the space of admissible history functions and initial states. Moreover, the initial value problem has to be formulated…
We investigate the stability properties of an abstract class of semi-linear systems. Our main result establishes rational rates of decay for classical solutions assuming a certain non-uniform observability estimate for the linear part and…
We propose a new approach to the study of (nonlinear) growth and instability for semilinear evolution equations with compact nonlinearities. We show, in particular, that compact nonlinear perturbations of a linear evolution equation can be…
Robust hyperbolicity and stability results for linear partial differential equations with delay will be given and, as an application, the effect of small delays to the asymptotic properties of feedback systems will be analyzed.
We give a proof for the asymptotic exponential stability of equilibria of quasilinear parabolic evolution equations in admissible interpolation spaces.
This paper investigates the exponential stability of abstract mean field systems in their synchronized state. We analyze stability by studying the linearized system and demonstrate the existence of an exponentially stable invariant…