A new insight into Serre's reduction problem

Thomas Cluzeau (1) , Alban Quadrat (2)

1 XLIM-DMI - DMI
2 DISCO - Dynamical Interconnected Systems in COmplex Environments

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] and [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.

Keywords: Mathematical systems theory.; Linear functional systems; Module theory; Serre's reduction; The factorization problem; Applications to hydrodynamics; The decomposition problem

Domains: Computer Science [cs]; Symbolic Computation [cs.SC]; Automatic; Analysis of PDEs [math.AP]

Thomas Cluzeau, Alban Quadrat. A new insight into Serre's reduction problem. Linear Algebra and its Applications, 2015, 483, pp.40-100. ⟨10.1016/j.laa.2015.04.035⟩. ⟨hal-01259834⟩