A new insight into Serre's reduction problem

作者：Cluzeau Thomas; Quadrat Alban^*

来源：Linear Algebra and Its Applications, 2015, 483: 40-100.

DOI：10.1016/j.laa.2015.04.035

• Mathematical systems theory
• Linear functional systems
• Module theory
• Serre's reduction
• The factorization problem
• The decomposition problem
• Applications to hydrodynamics

The purpose of this paper is to study the connections existing between Serre's reduction of linear functional systems which aims at finding an equivalent system defined by fewer equations and fewer unknowns - and the decomposition problem - which aims at finding an equivalent system having a diagonal block structure - in which one of the diagonal blocks is assumed to be the identity matrix. In order to do that, we further develop results on Serre's reduction problem and on the decomposition problem obtained in [2,3]. Finally, these techniques are used to analyze the decomposability of linear systems of partial differential equations studied in hydrodynamics such as the Oseen equations.

• 出版日期2015-10-15