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1.
Generalized Halanay inequalities for dissipativity of Volterra functional differential equations 总被引:1,自引:0,他引:1
Liping Wen Yuexin Yu Wansheng Wang 《Journal of Mathematical Analysis and Applications》2008,347(1):169-178
This paper is concerned with the dissipativity of theoretical solutions to nonlinear Volterra functional differential equations (VFDEs). At first, we give some generalizations of Halanay's inequality which play an important role in study of dissipativity and stability of differential equations. Then, by applying the generalization of Halanay's inequality, the dissipativity results of VFDEs are obtained, which provides unified theoretical foundation for the dissipativity analysis of systems in ordinary differential equations (ODEs), delay differential equations (DDEs), integro-differential equations (IDEs), Volterra delay-integro-differential equations (VDIDEs) and VFDEs of other type which appear in practice. 相似文献
2.
In this paper, we investigate the long time behavior of non-Fickian delay reaction-diffusion equations. These kinds of Volterra integro-differential equations are derived by combining a time memory term in the flux and a delay parameter in the reaction term. Energy estimates, dissipativity, asymptotic stability, and contractivity of the problems are obtained. Moreover, we prove that the numerical method discussed in the present paper has the ability to preserve stability and contractivity of the underlying systems. Some confirmations of these are illustrated by using the numerical method on two biological models. 相似文献
3.
This paper is concerned with the dissipativity of Volterra functional differential equations in a Hilbert space. A sufficient condition for dissipativity of one class of such equations is obtained. This result is applied to delay differential equations and integro-differential equations to obtain dissipativity results that are more general and deeper than related results in the previous literature. 相似文献
4.
Liping Wen Wansheng Wang Yuexin Yu 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(3-4):1746-1754
This paper is concerned with the dissipativity and asymptotic stability of the theoretical solutions of a class of nonlinear neutral delay integro-differential equations (NDIDEs). We first give a generalization of the Halanay inequality which plays an important role in the study of dissipativity and stability of differential equations. Then, we apply the generalization of the Halanay inequality to NDIDEs and the dissipativity and the asymptotic stability results of the theoretical solution of NDIDEs are obtained. From a numerical point of view, it is important to study the potential of numerical methods in preserving the qualitative behavior of the analytical solutions. Therefore, the results, presented in this paper, provide the theoretical foundation for analyzing the dissipativity and the asymptotic stability of the numerical methods when they are applied to these systems. 相似文献
5.
This paper is concerned with the numerical dissipativity of a class of nonlinear neutral delay integro-differential equations. The dissipativity results are obtained for algebraically stable Runge–Kutta methods when they are applied to above problems. 相似文献
6.
Dissipativity of the linearly implicit Euler scheme for Navier‐Stokes equations with delay
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Wansheng Wang 《Numerical Methods for Partial Differential Equations》2017,33(6):2114-2140
In this article, we study the dissipativity of the linearly implicit Euler scheme for the 2D Navier‐Stokes equations with time delay volume forces (NSD). This scheme can be viewed as an application of the implicit Euler scheme to linearized NSD. Therefore, only a linear system is needed to solve at each time step. The main results we obtain are that this scheme is L2 dissipative for any time step size and H1 dissipative under a time‐step constraint. As a consequence, the existence of a numerical attractor of the discrete dynamical system is established. A by‐product of the dissipativity analysis of the linearly implicit Euler scheme for NSD is that the dissipativity of an implicit‐explicit scheme for the celebrated Navier‐Stokes equations that treats the volume forces term explicitly is obtained.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 2114–2140, 2017 相似文献
7.
Yang Zhichun 《Annals of Differential Equations》2007,23(4):558-563
In this paper,we investigate the dissipativity behavior and give the range estimate for solutions of impulsive functional differential equations.Also,some criteria on asymptotical stability and exponential stability of the zero solution are obtained. 相似文献
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This paper is concerned with the numerical dissipativity of multistep Runge-Kutta methods for nonlinear Volterra delay-integro-differential equations.We investigate the dissipativity properties of (k,l)algebraically stable multistep Runge-Kutta methods with constrained grid and an uniform grid.The finitedimensional and infinite-dimensional dissipativity results of (k,l)-algebraically stable Runge-Kutta methods are obtained. 相似文献
10.
S. N. Vassilyev R. I. Kozlov S. A. Ul’yanov 《Proceedings of the Steklov Institute of Mathematics》2010,268(1):264-282
The issues of preserving dynamic properties when passing from a system of differential equations to another system obtained by a change of variables, as well as the issues of preserving the properties in the opposite direction, are considered. The potential of the reduction method, which was proposed earlier, in resolving these questions are demonstrated by the examples of such properties as stability, attraction, and dissipativity. Similar issues are investigated for the case when the second system is obtained in a way characteristic for the comparison method with vector Lyapunov functions. The application of one of the obtained dissipativity criteria to analyzing the nonlinear dynamics of a group of moving objects is considered. 相似文献
11.
This paper is concerned with the numerical dissipativity of nonlinear Volterra functional differential equations (VFDEs). We give some dissipativity results of Runge-Kutta methods when they are applied to VFDEs. These results provide unified theoretical foundation for the numerical dissipativity analysis of systems in ordinary differential equations (ODEs), delay differential equations (DDEs), integro-differential equations (IDEs), Volterra delay integro-differential equations (VDIDEs) and VFDEs of other type which appear in practice. Numerical examples are given to confirm our theoretical results. 相似文献
12.
研究一类积分微分方程线性多步方法(p,σ)的散逸性.当积分项用复合求积公式逼近时,证明了线性多步方法是有限维散逸的.这说明该方法很好地继承了系统本身所具有的重要性质.这一结论为数值求解这一类微分方程提供了更多的选择. 相似文献
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Tran Dinh Ke Lam Tran Phuong Thuy 《Mathematical Methods in the Applied Sciences》2020,43(15):8449-8465
We analyze the dissipativity and stability of solutions to a class of semilinear anomalous diffusion equations involving delays. The existence of absorbing set, the stability, and weak stability will be shown under suitable assumptions on the nonlinearity. Our analysis is based on new Halanay-type inequality, local estimates, and fixed-point arguments. 相似文献
15.
《随机分析与应用》2013,31(6):1577-1607
Abstract Linear and semilinear stochastic evolution equations with additive noise, where the forcing term is an infinite dimensional fractional Brownian motion are studied. Under usual dissipativity conditions the equations are shown to define random dynamical systems which have unique, exponentially attracting fixed points. The results are applied to stochastic parabolic PDE's. They are also applicable to standard finite-dimensional dissipative stochastic equation driven by fractional Brownian motion. 相似文献
16.
In this paper, the delay-dependent dissipativity of nonlinear delay differential equations is studied. A new dissipativity criterion is derived, which is less conservative than those in the existing literature in some cases, especially for equations with small delays. 相似文献
17.
Hong-jiong Tian 《计算数学(英文版)》2003,21(6):715-726
This paper deals with analytic and numerical dissipativity and exponential stability of singularly perturbed delay differential equations with any bounded state-independent lag. Sufficient conditions will be presented to ensure that any solution of the singularly perturbed delay differential equations (DDEs) with a bounded lag is dissipative and exponentially stable uniformly for sufficiently small ε > 0. We will study the numerical solution defined by the linear θ-method and one-leg method and show that they are dissipative and exponentially stable uniformly for sufficiently small ε > 0 if and only if θ = 1. 相似文献
18.
本文讨论多比例延迟微分方程的散逸性,给出了多比例延迟微分方程是散逸的充分条件,它可视为文献[8]中相应结果的推广。 相似文献
19.
N. Tatar 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2013,48(6):285-296
In this paper we consider a Kirchhoff type viscoelastic problem, and prove uniform stability of the system. We do not rely on the dissipativity of the system or the boundedness of the energy as in the previous treatments. There appears a quadratic term which we cannot estimate by the initial energy as our system is not clearly dissipative in advance. 相似文献
20.
Ying-Chin Su 《Journal of Differential Equations》2011,250(9):3668-3700
This research explores the Cauchy problem for a class of quasi-linear wave equations with time dependent sources. It can be transformed into the Cauchy problem of hyperbolic integro-differential systems of nonlinear balance laws. We introduce the generalized Glimm scheme in new version and study its stability which is proved by Glimm-type interaction estimates in a dissipativity assumption. The generalized solutions to the perturbed Riemann problems, the building blocks of generalized Glimm scheme, are constructed by Riemann problem method modeled on the source free equations. The global existence for the Lipschitz continuous solutions and weak solutions to the systems is established by the consistency of scheme and the weak convergence of source. Finally, the weak solutions are also the entropy solutions which satisfy the entropy inequality. 相似文献