数学物理学报(英文版) ›› 2001, Vol. 21 ›› Issue (1): 77-92.

• 论文 • 上一篇    下一篇

SOLVABILITY OF HIGHER INDEX TIME-VARYING LINEAR DIFFERENTIAL-ALGEBRAIC EQUATIONS

 宋永忠   

  1. School of Mathematics and Computer Science, Nanjing Normal University, Nanjing 210097, China.
  • 出版日期:2001-01-06 发布日期:2001-01-06
  • 基金资助:

    Project supported by the National Natural Science Foundation of China and by Jiangsu Provincial Natural Science Foundation

SOLVABILITY OF HIGHER INDEX TIME-VARYING LINEAR DIFFERENTIAL-ALGEBRAIC EQUATIONS

 SONG Yong-Zhong   

  1. School of Mathematics and Computer Science, Nanjing Normal University, Nanjing 210097, China.
  • Online:2001-01-06 Published:2001-01-06
  • Supported by:

    Project supported by the National Natural Science Foundation of China and by Jiangsu Provincial Natural Science Foundation

摘要:

Linear differential-algebraic equations (DAEs) with time-varying coefficients A(t)x′(t) + B(t)x(t) = q(t), which are tractable with a higher index, are discussed. Their essential properties are investigated. Some equivalent systems are given. Using them the paper shows how to state properly initial and boundary conditions for these DAEs. The existence and uniqueness theory of the solution of the initial and boundary value problems
for higher index DAEs are proposed.

关键词: Differential-algebraic equations, index, solvability, existence, uniqueness

Abstract:

Linear differential-algebraic equations (DAEs) with time-varying coefficients A(t)x′(t) + B(t)x(t) = q(t), which are tractable with a higher index, are discussed. Their essential properties are investigated. Some equivalent systems are given. Using them the paper shows how to state properly initial and boundary conditions for these DAEs. The existence and uniqueness theory of the solution of the initial and boundary value problems
for higher index DAEs are proposed.

Key words: Differential-algebraic equations, index, solvability, existence, uniqueness

中图分类号: 

  • 65L05