微分代数方程去奇异化分析  

Desingularizing of Differential-Algebraic Equations

作　　者：邹杰涛[1] 王瑞瑞[1] 杨志辉[1] 

机构地区：[1]北方工业大学理学院,北京100144

出　　处：《数学的实践与认识》2011年第18期230-235,共6页Mathematics in Practice and Theory

基　　金：北京市自然基金(1082007);北京市教委面上项目(KM200410009010);北京市中青年骨干项目(PHR201008199)

摘　　要：利用去奇异化方法讨论了拟线性微分代数方程在奇点邻域内光滑解的性质.通过尺度参数的微分同胚变换,将拟线性微分代数方程转化为相应的常微分方程,从而构造出在孤立奇点邻域内的初始微分代数方程的光滑解,给出解存在的充分条件,并进一步讨论了解的性质.In this paper we use the desingularizing method to discuss smooth solutions of quasi-linear differential-algebraic equations （DAEs） in the neighborhood of singularities. Through a diffeomorphic transformation of the scale parameter, the original quasi-linear DAEs can be changed into a corresponding ODE from which we can construct smooth solutions of DAEs near the isolate singularities. Furthermore, a sufficient condition for the existence of smooth solutions of quasi-linear differential-algebraic equations is presented.

关 键 词：微分代数方程 去奇异化 几何奇点 

分 类 号：O155[理学—数学]