Serre's reduction of linear functional systems

Serre's reduction aims at reducing the number of unknowns and equations of a linear functional system (e.g., system of partial differential equations, system of differential time-delay equations, system of difference equations). Finding an equivalent representation of a linear functional system containing fewer equations and fewer unknowns generally simplifies the study of its structural properties, its closed-form integration as well as of different numerical analysis issues. The purpose of this paper is to present a constructive approach to Serre's reduction for determined and underdetermined linear functional systems

Further Results on the Decomposition and Serre's Reduction of Linear Functional Systems

International audienc

A new insight into Serre's reduction problem

International audienceThe 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

Un nouveau point de vue sur le problème de réduction de Serre

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 previously obtained. Finally, we show how these techniques can be used to analyze the decomposability problem of standard linear systems of partial differential equations studied in hydrodynamics such as Stokes equations, Oseen equations and the movement of an incompressible fluid rotating with a small velocity around the vertical axis