一类多服务排队系统正解的存在性与渐进稳定性

运用算子半群理论讨论了一类多服务排队系统正解的存在唯一性,并证明了所得的半群为Markov半群.另外,进一步得到了系统的稳态解是渐进稳定的.     

Necessary and sufficient conditions for the regularity and stability for some partial functional differential equations with infinite delay

In this work we give necessary and sufficient conditions for the regularity and stability of solutions for some partial functional differential equations with infinite delay. We establish also a new characterization of the infinitesimal generator of the solution semigroup.     

Necessary and sufficient conditions for the regularity and stability of solutions for some partial neutral functional differential equations with infinite delay

In this paper we give necessary and sufficient conditions for the regularity and stability of solutions for some partial neutral functional differential equations with infinite delay. We establish also a generalization and extension of the characterization of the infinitesimal generator of the solution semigroup. To illustrate our abstract results, we study the stability of the neutral Lotka-Volterra model with diffusion.     

具一组可修复设备的系统解的适定性和稳定性

研究具一组可修复设备的系统解的适定性和稳定性.使用泛函分析方法,特别是Banach空间上的线性算子理论和C_0半群理论,证明了系统解的适定性以及正解的存在性,证明了系统解的渐近稳定性,指数稳定性以及严格占优本征值的存在性,证实了实际问题中相关假设的合理性.     

Asymptotic behaviour of a quasilinear hyperbolic equation with hysteresis

The paper deals with the asymptotic behaviour of the solution of a quasilinear hyperbolic equation with hysteresis. A stability result for solution in L¹(Ω) is derived by the nonlinear semigroup approach.     

On the nonnegative self-adjoint solutions of the operator Riccati equation for infinite dimensional systems

The nonnegative self-adjoint solutions of the operator Riccati equation (ORE) are studied for stabilizable semigroup Hilbert state space systems with bounded sensing and control. Basic properties of the maximal solution of the ORE are investigated: stability of the corresponding closed loop system, structure of the kernel, Hilbert-Schmidt property. Similar properties are obtained for the nonnegative self-adjoint solutions of the ORE. The analysis leads to a complete classification of all nonnegative self-adjoint solutions, which is based on a bijection between these solutions and finite dimensional semigroup invariant subspaces contained in the antistable unobservable subspace.     

Some remarks on the asymptotic behavior of the semigroup associated with age-structured diffusive populations

We consider linear age-structured population equations with diffusion. Supposing maximal regularity of the diffusion operator, we characterize the generator and its spectral properties of the associated strongly continuous semigroup. In particular, we provide conditions for stability of the zero solution and for asynchronous exponential growth.     

Mindlin–Timoshenko systems with Kelvin–Voigt: analyticity and optimal decay rates

This paper is concerned with asymptotic stability of Mindlin–Timoshenko plates with dissipation of Kelvin–Voigt type on the equations for the rotation angles. We prove that the corresponding evolution semigroup is analytic if a viscoelastic damping is also effective over the equation for the transversal displacements. On the contrary, if the transversal displacement is undamped, we show that the semigroup is neither analytic nor exponentially stable. In addition, in the latter case, we show that the solution decays polynomially and we prove that the decay rate found is optimal.     

Stability Conditions for Abstract Functional Differential Equations in Hilbert Space

Abstract. Stability conditions for functional differential equations of the form: du (t)/ dt = Au(t)+ bAu(t-h)+(a^\ast Au)(t) are studied, where A is the infinitesimal generator of an analytic semigroup in a Hilbert space, b\neq 0 and the convolution term contains a square integrable real function a\neq 0 . Norm discontinuity of the solution semigroup of the equation with discrete delay is avoided by studying the inverse of the characteristic operator. Sufficient and necessary conditions for the uniform exponential stability of the solution semigroup are obtained. The results are applied to a retarded partial integrodifferential equation.     

一般迁移方程相应余项的弱紧性及其应用

在L¹空间,研究了板几何中一类具周期边界条件的各向异性、连续能量、均匀介质的迁移方程.通过构造算子,利用比较算子方法,证明了该迁移算子A相应的迁移半群V(t)(t≥0)的Dyson-Phillips展开式的伽阶余项R_n(t)(n≥1)的弱紧性,得到了半群V(t)与U(t)(streaming算子B产生)本质谱相同,本质谱型一致;迁移算子A的谱在区域Γ中由有限个具有限代数重数的离散本征值组成;迁移方程解的渐近稳定性.     

一类串联动态修复系统的适定性

本文讨论了一类串联动态修复系统的数学模型 ,用泛函分析中 C0 半群的方法证明了该系统的非负解的存在唯一性 ,并且进一步在一定条件下给出了其解是半稳定的     

板几何中奇异迁移方程解的渐近稳定性

在L~p(1p+∞)空间,研究了板几何中一类具反射边界条件的各向异性、连续能量、均匀介质的奇异迁移方程,通过构造算子,利用比较算子方法,证明了奇异迁移算子A相应的奇异迁移半群V(t)(t≥0)的Dyson-Phillips展开式的一阶余项R_1(t)的紧性,得到了半群V(t)与U(t)(streaming算子B产生)本质谱相同,本质谱型一致;迁移算子A的谱在区域T中由有限个具有限代数重数的离散本征值组成;迁移方程解的渐近稳定性.     

On the decay of solutions in nonsimple elastic solids with memory

The decay of solutions in nonsimple elasticity with memory is addressed, analyzing how the decay rate is influenced by the different dissipation mechanisms appearing in the equations. In particular, a first order dissipation is shown to guarantee the asymptotic stability of the related solution semigroup, but is not strong enough to entail exponential stability. The latter occurs for a dissipation mechanism of the second order, that is, the same order as the one of the leading operator.     

Extensions of linear systems to duals of countably Hilbertian spaces with graph topology

The state space for an infinite-dimensional system of the form = Ax + Bu can be extended to the dual of a countably Hilbertainspace with graph toplogy. The Study of countably Hilbertianspaces with graph topology and their duals is made. The structuresof the extensions of a C₀ semigroup and the stability theoryof the restrictions and extensions of the semigroup are illustrated.An existence and uniqueness theorem of the solution of the extendedsystem is given.     

一类串联可修复系统指数稳定性

运用泛函分析的方法和线性算子半群理论,证明了严格占优本征值的存在性,并通过分析系统本质谱界经过扰动后的变化,进一步表明在一定的条件下,系统的动态解的指数形式收敛于系统的稳态解.     

一类Schrodinger方程的周期解和谱方法

本文利用半群理论讨论了一类非线性非自共轭Ｓｃｈｒｏｄｉｎｇｅｒ方程周期初边值解的存在唯一性，以及它的Ｆｏｕｒｉｅｒ谱方法的可解性，稳定性和收敛性     

The Strong Stability and Instability of a Fluid-Structure Semigroup

The strong stability problem for a fluid-structure interactive partial differential equation (PDE) is considered. The PDE comprises a coupling of the linearized Stokes equations to the classical system of elasticity, with the coupling occurring on the boundary interface between the fluid and solid media. Because of the nature of the unbounded coupling between fluid and structure, the resolvent of the associated semigroup generator will not be a compact operator. In consequence, the classical solution to the stability problem, by means of the Nagy-Foias decomposition, will not avail here. Moreover, it is not practicable to write down explicitly the resolvent of the fluid-structure generator; this situation thus makes it problematic to use the well-known semigroup stability result of Arendt-Batty and Lyubich-Phong. When a locally supported boundary dissipative mechanism is in place, we derive here a result of strong decay for this fluid-structure PDE. In the absence of said dissipative mechanism, we show the lack of asymptotic decay for solutions corresponding to arbitary initial data of finite energy.     

Positivity and stability of linear functional differential equations with infinite delay

General linear functional differential equations with infinite delay are considered. We first give an explicit criterion for positivity of the solution semigroup of linear functional differential equations with infinite delay and then a Perron‐Frobenius type theorem for positive equations. Next, a novel criterion for the exponential asymptotic stability of positive equations is presented. Furthermore, two sufficient conditions for the exponential asymptotic stability of positive equations subjected to structured perturbations and affine perturbations are provided. Finally, we applied the obtained results to problems of the exponential asymptotic stability of Volterra integrodifferential equations. To the best of our knowledge, most of the results of this paper are new.     

Stability conditions for abstract functional differential equations in Hilbert space

Stability conditions for functional differential equations of the form: du(t)/dt = Au(t) + bAu(t ? h) + (a* Au)(t) are studied, where A is the infinitesimal generator of an analytic semigroup in a Hilbert space, b ≠ 0 and the convolution term contains a square integrable real function a ≠ 0. Norm discontinuity of the solution semigroup of the equation with discrete delay is avoided by studying the inverse of the characteristic operator. Sufficient and necessary conditions for the uniform exponential stability of the solution semigroup are obtained. The results are applied to a retarded partial integrodifferential equation.     

具有预警功能的热储备可修复平行系统

在热储备可修复平行系统的基础上,增加了一个预警状态,使其变为预警系统,使得系统的初值条件属于定义域,从而由线性算子半群方法求得的弱解变为强解,并研究了系统的稳定性,同时当风险系数λ_c。趋于无穷大时对预警系统和非预警系统的稳态可用度进行了分析.