CAJ | 학술논문

从动力系统的角度研究微分代数系统, 利用单调流理论中的结果和方法讨论微分代数系统渐近性态. 首先, 我们把所考察的系统嵌入到一族相关的系统, 引进使得系统族中的每个系统生成单调流的相应偏序和条件. 然后给出了若干关于解收敛于平衡点的一般性结果, 并对一类微分代数系统的渐近性作了较为精细的讨论. 我们的结果是Hirch等关于常微分方程的相关结果的推广和改进.
종동력계통적각도연구미분대수계통, 이용단조류이론중적결과화방법토론미분대수계통점근성태. 수선, 아문파소고찰적계통감입도일족상관적계통, 인진사득계통족중적매개계통생성단조류적상응편서화조건. 연후급출료약간관우해수렴우평형점적일반성결과, 병대일류미분대수계통적점근성작료교위정세적토론. 아문적결과시Hirch등관우상미분방정적상관결과적추엄화개진.
This paper is devoted to discussing asymptotic behaviors for algebraic-differential systems by the use of the monotone flow theory. First ofall, a differential-algebraic system is imbedded into the entire familyof the systems, and a partial order and the conditions are introducedsuch that the flow is monotone for each of the family. We then obtainsome general results such that solution of each system to such a familyconverges to equilibrium, and the asymptotic behaviors of a system arediscuseed in some detail. Our results have generalized and improved someresults shown in ordinary differential equations by Hirch et al.