Systems with distributions and viability theorem

The approach to the consideration of the ordinary differential equations with distributions in the classical space D^′ of distributions with continuous test functions has certain insufficiencies: the notations are incorrect from the point of view of distribution theory, the right-hand side has to satisfy the restrictive conditions of equality type. In the present paper we consider an initial value problem for the ordinary differential equation with distributions in the space of distributions with dynamic test functions T^′, where the continuous operation of multiplication of distributions by discontinuous functions is defined [V. Derr, D. Kinzebulatov, Distributions with dynamic test functions and multiplication by discontinuous functions, preprint, arXiv: math.CA/0603351, 2006], and show that this approach does not have the aforementioned insufficiencies. We provide the sufficient conditions for viability of solutions of the ordinary differential equations with distributions (a generalization of the Nagumo Theorem), and show that the consideration of the distributional (impulse) controls in the problem of avoidance of encounters with the set (the maximal viability time problem) allows us to provide for the existence of solution, which may not exist for the ordinary controls.     

一类具有周期脉冲的差分系统的汽车近稳定性

建立了-类具有常系数周期脉冲的差分系统,得到了该常数脉冲系统周期解存在且渐近稳定的充分条件,最后把此研究方法应用到文[6]当中也同样适用,并简化了证明过程.     

An impulse technique of measuring insertion loss of open screens

An impulse response technique has been investigated by application to the open screens for obtaining sound transmission loss. The measurements of such screens according to ISO 140 were also presented. The predicted results calculated by a model which is based on Huygen's principle and Kirchhoff's formulation have shown good agreements with the results obtained by impulse method. The method requires no specialist acoustic facilities and measurement systems can be portable.     

Existence of Solutions for Impulsive Parabolic Partial Differential Equations

We discuss the propagation of heat along a homogeneous rod of length A under the influence of a nonlinear heat source and impulsive effects at fixed times. This problem is described by an initial-boundary value problem for a nonlinear parabolic partial differential equation subjected to impulsive effects at fixed times. Using Green's function, we convert the problem into a nonlinear integral equation. Sufficient conditions are provided that enable the application of fixed point theorems to prove existence and uniqueness of solutions.     

非线性分数阶微分方程脉冲反周期边值问题

本文研究q∈(0,1]的分数阶非线性微分方程的脉冲反周期边值问题的解的存在唯一性,我们利用Altman's不动点定理和Leray-Schauder's不动点定理来证明.     

具有脉冲输入和资源循环的恒化器模型

研究了一类在污染环境下的具有脉冲输入和资源循环的Monod型恒化器模型,利用Floquet定理和脉冲微分方程解的比较定理,我们得出了系统的微生物灭绝周期解全局渐近稳定以及系统持久的充分条件.     

Osillation criteria for impulsive parobolic systems *

This paper considers a class of nonlinear impulsive parabolic systems. By using impulsive differential inequalities,We establish several oscillation criteris for such systems subject to two different boundary conditions.     

Asymptotic behavior of solutions for nonlinear delay differential equation with impulses

This paper studies the asymptotic behavior of solutions of the nonlinear delay differential equation with impulses

     

Existence and global exponential stability of periodic solution for impulsive Cohen-Grossberg-type BAM neural networks with continuously distributed delays

This paper is concerned with the existence and global exponential stability of periodic solution for a class of impulsive Cohen-Grossberg-type BAM neural networks with continuously distributed delays. Some sufficient conditions ensuring the existence and global exponential stability of periodic solution are derived by constructing a suitable Lyapunov function and a new differential inequality. The proposed method can also be applied to study the impulsive Cohen-Grossberg-type BAM neural networks with finite distributed delays. The results in this paper extend and improve the earlier publications. Finally, two examples with numerical simulations are given to demonstrate the obtained results.     

Approximate solution to the diffusion equation and its application to seepage-related problems

Effective dam safety procedures require pore pressure measurements to be interpreted as soon as possible after readings have been taken. Direct interpretations based on partial differential equations are not appropriate. Here, we took a different approach which consisted in applying the impulse response function concept to a dam site. Consequently, two models were designed so that their parameters matched the temporal moments of Green’s function of the associated parabolic problem. These models were compared with closed-form solutions. The first model was the exponential decay model, which gave good results, but did not account for high loading harmonics. The second model, based on the fundamental solution of a parabolic problem, was surprisingly accurate. As an example problem we considered monitoring data obtained from a zoned earth dam. The results show that the main aspects of the processes reflected in most cell recordings can be described in a linear framework, and that they are accounted for by both models.