Related papers: Exponential decay for negative feedback loop with …
A condition which guaranties the exponential decay of the solutions of the initial-boundary value problem for the damped wave equation is proved. A method for the effective computability of the coefficient of exponential decay is also…
In this paper correspondence between experimental data for packet delay and two theoretical types of distribution is investigated. Calculations have shown that the exponential distribution describes the data on network delay better, than…
In this work, we are concerned with a nonlinear wave equation with variable exponents. A distributive delay is imposed into the damping term with variable exponents nonlinearity. Firstly, we show that the global nonexistence time can be…
This paper proposes a unified approach for studying global exponential stability of a general class of switched systems described by time-varying nonlinear functional differential equations. Some new delay-independent criteria of global…
In this work, we consider the existence of global solution and the exponential decay of a nonlinear porous elastic system with time delay. The nonlinear term as well as the delay acting in the equation of the volume fraction. In order to…
In this article, a generalized version of Negative binomial-beta exponential distribution with five parameters have been introduced. Some interesting submodels have been derived from it. A comprehensive mathematical treatment of proposed…
This note studies the exponential convergence of input-output signals of discrete-time nonlinear systems composed of a feedback interconnection of a linear time-invariant system and a nonlinear uncertainty. Both the open-loop subsystems are…
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…
We consider the linear growth-fragmentation equation arising in the modelling of cell division or polymerisation processes. For constant coefficients, we prove that the dynamics converges to the steady state with an exponential rate. The…
We consider abstract semilinear evolution equations with a time delay feedback. We show that, if the $C_0$-semigroup describing the linear part of the model is exponentially stable, then the whole system retains this good property when a…
We formulate a coherent approach to signals and systems theory on time scales. The two derivatives from the time-scale calculus are used, i.e., nabla (forward) and delta (backward), and the corresponding eigenfunctions, the so-called nabla…
We prove optimal decay estimates for positive solutions to elliptic p-Laplacian problems in the entire Euclidean space, when a critical nonlinearity with a decaying source term is considered. Also gradient decay estimates are furnished. Our…
We prove optimal estimates for the decay in time of solutions to a rather general class of non-local in time subdiffusion equations in $\mathbb{R}^d$. An important special case is the time-fractional diffusion equation, which has seen much…
Exponential stability of the second order linear delay differential equation in $x$ and $u$-control $$ \ddot{x}(t)+a_1(t)\dot{x}(h_1(t))+a_2(t)x(h_2(t))+a_3(t)u(h_3(t))=0 $$ is studied, where indirect feedback control…
Using energy methods, we prove some power-law and exponential decay estimates for classical and nonlocal evolutionary equations. The results obtained are framed into a general setting, which comprise, among the others, equations involving…
Periodic patterns in dynamical behaviours of biological models described by simple form differential delay equations are studied. Mathematical models are given by a class of scalar delay differential equations with a multiplicative time…
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.…
We establish a new criterion for exponential mixing of random dynamical systems. Our criterion is applicable to a wide range of systems, including in particular dispersive equations. Its verification is in nature related to several topics,…
This paper deals with the exponential separation of type II, an important concept for random systems of differential equations with delay, introduced in \JM\ et al.~\cite{MiNoOb1}. Two different approaches to its existence are presented.…
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…