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We consider several classes of degenerate hyperbolic equations involving delay terms and suitable nonlinearities. The idea is to rewrite the problems in an abstract way and, using semigroup theory and energy method, we study well posedness…
Understanding how time delays impact the stability of a delay differential equation is important for modeling many natural and technological systems that experience time delays. Here we introduce a new stability criterion for…
This article concerns the nonlinear Korteweg-de Vries equation with boundary time-delay feedback. Under appropriate assumption on the coefficients of the feedbacks (delayed or not), we first prove that this nonlinear infinite dimensional…
A simple non-autonomous scalar differential equation with delay, exponential decay, nonlinear negative feedback and a periodic multiplicative coefficient is considered. It is shown that stable slowly oscillating periodic solutions with the…
We study the time-asymptotic behavior of linear hyperbolic systems under partial dissipation which is localized in suitable subsets of the domain. More precisely, we recover the classical decay rates of partially dissipative systems…
In this paper, stability analysis of time delay systems is considered based on decomposition of the systems to subsystems. The decomposition process needs matrices of these systems to be simultaneously block triangularize. We show that a…
Feedback delay has been identified as a key ingredient in the quorum sensing synchronization of synthetic gene oscillators. While this influence has been evidenced at the theoretical level in a simplified system of degrade-and-fire…
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 article, we investigate the existence and properties of time-periodic solutions for damped evolutionary partial differential equations subject to periodic forcing. Particular emphasis is placed on configurations where the energy…
Recently, the following novel method for proving the existence of solutions for certain linear time-invariant PDEs was introduced: The operator associated to a given PDE is represented by a (larger) operator with an internal loop. If the…
In this paper we analyze a semilinear abstract damped wave-type equation with time delay. We assume that the delay feedback coefficient is variable in time and belonging to $L^1_{loc}([0, +\infty)).$ Under suitable assumptions, we show…
We study the stability of general $n$-dimensional nonautonomous linear differential equations with infinite delays. Delay independent criteria, as well as criteria depending on the size of some finite delays are established. In the first…
We consider an evolution equation whose time-diffusion is of fractional type and we provide decay estimates in time for the $L^s$-norm of the solutions in a bounded domain. The spatial operator that we take into account is very general and…
This paper investigates the stability properties of a nonlinear fractional differential equation with two discrete delays and a delay-dependent coefficient. Such equations arise in various biological and control systems where temporal…
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…
A nonlinear inequality is formulated in the paper. An estimate of 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. It can be…
We investigate some structural properties of an efficient feedback law that stabilize linear time-reversible systems with an arbitrarily large decay rate. After giving a short proof of the generation of a group by the closed-loop operator,…
The paper concerns a class of $n$-dimensional non-autonomous delay differential equations obtained by adding a non-monotone delayed perturbation to a linear homogeneous cooperative system of ordinary differential equations. This family…
Dynamic systems described by differential equations often involve feedback among system components. When there are time delays for components to sense and respond to feedback, delay differential equation (DDE) models are commonly used. This…
It is known that input-output approaches based on scaled small-gain theorems with constant $D$-scalings and integral linear constraints are non-conservative for the analysis of some classes of linear positive systems interconnected with…