On the Index and the Order of Quasi-regular Implicit Systems of Differential Equations
Commutative Algebra
2008-11-19 v2 Classical Analysis and ODEs
Abstract
This paper is mainly devoted to the study of the differentiation index and the order for quasi-regular implicit ordinary differential algebraic equation (DAE) systems. We give an algebraic definition of the differentiation index and prove a Jacobi-type upper bound for the sum of the order and the differentiation index. Our techniques also enable us to obtain an alternative proof of a combinatorial bound proposed by Jacobi for the order. As a consequence of our approach we deduce an upper bound for the Hilbert-Kolchin regularity and an effective ideal membership test for quasi-regular implicit systems. Finally, we prove a theorem of existence and uniqueness of solutions for implicit differential systems.
Keywords
Cite
@article{arxiv.0804.4842,
title = {On the Index and the Order of Quasi-regular Implicit Systems of Differential Equations},
author = {Lisi D'Alfonso and Gabriela Jeronimo and Gustavo Massaccesi and Pablo Solernó},
journal= {arXiv preprint arXiv:0804.4842},
year = {2008}
}