基于脉冲和时滞效应的拟线性双曲系统的(强)振动性分析  

(Strong)Oscillation Analysis of Quasilinear Hyperbolic Systems Based on Effect of Impulse and Delay

作　　者：罗李平[1] 罗振国[1] 曾云辉[1] 

机构地区：[1]衡阳师范学院数学与统计学院,湖南衡阳421002

出　　处：《中国海洋大学学报（自然科学版）》2016年第4期149-152,共4页Periodical of Ocean University of China

基　　金：湖南省"十二五"重点建设学科项目(湘教发[2011]76号);湖南省普通高校青年骨干教师培养对象项目(湘教通[2015]361号);湖南省自然科学基金面上项目(2016JJ2008)资助~~

摘　　要：脉冲偏微分系统能够成功地应用于力学、理论物理、化学及人口动力学、生物工程、最优控制和经济学等方面的数学模拟。振动性理论作为脉冲偏微分系统定性理论的重要分支之一,对其进行研究具有极大的理论意义与实用价值。本文考虑一类基于脉冲和时滞效应的拟线性双曲系统的(强)振动性问题,直接从(强)振动的定义出发,借助新的处理拟线性扩散项的技巧、Green散度定理和第二类边界条件把这类系统解的振动问题转化为脉冲时滞微分不等式不存在最终正解的问题,并利用二阶脉冲时滞微分不等式的某些结果,建立了该类系统在第二类边界条件下所有有界解(强)振动的若干充分判据,结论充分地表明系统振动是由脉冲量和时滞量引起的,"强振动性"的判别条件比"振动性"的判别条件更强些。Impulsive partial differential systems can be successfully used for mathematical simulation in mechanics,theory physics,chemistry,population dynamics,biotechnology,optimal control and economics,etc.The oscillation theory is the one of the important branches of qualitative theory of impulsive partial differential systems.Therefore,it is of great theoretical and practical value to research the oscillation of partial functional differential equations.In this paper,the（strong）oscillation problems for a class of quasilinear hyperbolic systems based on the effect of impulse and delay are considered.Starting from the definition of oscillation directly,the oscillatory problems to the systems are reduced to the problem of which impulsive delay differential inequality hasn＇t eventually position solution by employing a new technique of treating quasilinear diffusion term and Green＇s divergence theorem and second boundary condition,and thereby some sufficient criteria are obtained for the（strong）oscillation of all bounded solutions of such systems under second boundary condition via some results of second order impulsive delay differential inequality.The conclusions fully indicate that the system oscillation are caused by impulse and delay,and the criterion of strong oscillation is more sharp than the one of oscillation.

关 键 词：双曲系统 (强)振动性 拟线性扩散项 脉冲 时滞 

分 类 号：O175.27[理学—数学]