相关论文: Bohl-Perron type stability theorems for linear dif…
Detailed study of spectral properties and of linear stability is presented for a class of lattice Boltzmann models with a non-ideal equation of state. Examples include the van der Waals and the shallow water models. Both analytical and…
In this paper we deal with infinite-dimensional nonlinear forward complete dynamical systems which are subject to external disturbances. We first extend the well-known Datko lemma to the framework of the considered class of systems. Thanks…
This note places primary emphasis on improving the asymptotic behavior of a multi-dimensional delayed wave equation in the absence of any displacement term. In the first instance, the delay is assumed to occur in the boundary. Then,…
In this paper, we establish the existence of a positive, bounded solution for a class of parabolic partial differential equations with nonlinear boundary conditions, where the boundary conditions depend on the solution on the boundary at a…
We study integral-to-integral input-to-state stability for infinite-dimensional linear systems with inputs and trajectories in $L^p$-spaces. We start by developing the corresponding admissibility theory for linear systems with unbounded…
This paper studies the moment boundedness of solutions of linear stochastic delay differential equations with distributed delay. For a linear stochastic delay differential equation, the first moment stability is known to be identical to…
We consider second-order evolution equations in an abstract setting with intermittently delayed/ not-delayed damping. We give sufficient conditions for asymptotic and exponential stability, improving and generalising our previous results…
We review $H^{1}$-well-posedness for initial value problems of ordinary differential equations with state-dependent right-hand side. We streamline known approaches to infer existence and uniqueness of solutions for small times given a…
In this paper, we investigate the well-posedness and asymptotic behavior of difference equations of the form $x(t) = A x(t - \tau(t))$, $t \geq 0$, where the unknown function $x$ takes values in $\mathbb R^d$ for some positive integer $d$,…
The input/output stability of an interconnected system composed of an ordinary differential equation and a damped string equation is studied. Issued from the literature on time-delay systems, an exact stability result is firstly derived…
In this paper, we discuss delayed periodic dynamical systems, compare capability of criteria of global exponential stability in terms of various $L^{p}$ ($1\le p<\infty$) norms. A general approach to investigate global exponential stability…
We consider a Hamiltonian systems which is invariant under a one-parameter unitary group. We give a criterion for the stability and instability of bound states for the degenerate case. We apply our theorem to the single power nonlinear…
In this paper exponential stability of nonlinear fractional order stochastic system with Poisson jumps is studied in finite dimensional space. Existence and uniqueness of solution, stability and exponential stability results are established…
We prove the equivalence of the well-posedness of a partial differential equation with delay and an associated abstract Cauchy problem. This is used to derive sufficient conditions for well-posedness, exponential stability and norm…
We study an interplay between delay and discontinuous hysteresis in dynamical systems. After having established existence and uniqueness of solutions, we focus on the analysis of stability of periodic solutions. The main object we study is…
Recent results in the literature provide computational evidence that stabilized semi-implicit time-stepping method can efficiently simulate phase field problems involving fourth-order nonlinear dif- fusion, with typical examples like the…
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.
PDEs with periodic boundary conditions are frequently used to model processes in large spatial environments, assuming solutions to extend periodically beyond some bounded interval. However, solutions to these PDEs often do not converge to a…
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…
We study the rate of decay of correlations for equilibrium states associated to a robust class of non-uniformly expanding maps where no Markov assumption is required. We show that the Ruelle-Perron-Frobenius operator acting on the space of…