Related papers: Energy decay for evolution equations with delay fe…
In this paper we consider second order evolution equations with unbounded dynamic feedbacks. Under a regularity assumption we show that observability properties for the undamped problem imply decay estimates for the damped problem. We…
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 consider a class of evolution equations describing population dynamics in the presence of a carrying capacity depending on the population with delay. In an earlier work, we presented an exhaustive classification of the logistic equation…
In this paper, we study the positivity and (uniform) exponential stability of a large class of perturbed semigroups. Our approach is essentially based on the feedback theory of infinite-dimensional linear systems. The obtained results are…
While the asymptotic stability of positive linear systems in the presence of bounded time delays has been thoroughly investigated, the theory for nonlinear positive systems is considerably less well-developed. This paper presents a set of…
We study the damped wave equation with a damping coefficient which is possibly singular and unbounded at infinity. In general, zero belongs to the spectrum of the corresponding generator, which prevents a uniform (exponential) decay for the…
We consider second-order evolution equations in an abstract setting with damping and time delay and give sufficient conditions ensuring exponential stability. Our abstract framework is then applied to the wave equation, the elasticity…
The celebrated Mackey-Glass model describes the dynamics of physiological \textit{delayed} systems in which the actual evolution depends on the values of the variables at some \textit{previous} times. This kind of systems are usually…
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…
Self-regulatory models are common in nature, as described e.g. in (\cite{mur}), (\cite{ha}) and (\cite{Gb}).\\ Let us consider a system made up of a number of glands as a motivation. Each gland secretes a hormone that allows secretion in…
Delayed processes are ubiquitous in biological systems and are often characterized by delay differential equations (DDEs) and their extension to include stochastic effects. DDEs do not explicitly incorporate intermediate states associated…
We study the well-posedness of nonautonomous nonlinear delay equations in $\mathbb{R}^{n}$ as evolutionary equations in a proper Hilbert space. We present a construction of solving operators (nonautonomous case) or nonlinear semigroups…
In this paper, we consider energy decay estimates for the following nonlinear evolution problem $$\begin{split} [P(u_t(t))]_t + A u(t) + B(t , x , u_t(t)) =0,\quad t\in J=(0,\infty), \end{split}$$ under suitable assumptions on the…
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…
Although the theory of density evolution in maps and ordinary differential equations is well developed, the situation is far from satisfactory in continuous time systems with delay. This paper reviews some of the work that has been done…
In this work, we study the stabilization of the wave equation using an internal delayed potential. Interestingly, the stabilization mechanism is entirely induced by the delay, since exponential stabilization cannot be achieved in its…
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…
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…
A quadratic inequality is formulated in the paper. An estimate on the rate of decay of solutions to this inequality is obtained. This inequality is of interest in a study of dynamical systems and nonlinear evolution equations.
A degenerate wave equation with time-varying delay in the boundary control input is considered. The well-posedness of the system is established by applying the semigroup theory. The boundary stabilization of the degenerate wave equation is…