A bound for a typical differential dimension of system of linear differential equations

TL;DR

This paper establishes bounds on the typical differential dimension of systems of linear partial differential equations, specifically focusing on the leading coefficient of the Kolchin dimension polynomial in codimension two.

Contribution

It provides the first known bounds for the leading coefficient of the Kolchin dimension polynomial in this context.

Findings

Upper and lower bounds for the leading coefficient are derived.

Results apply specifically to systems in codimension two.

The bounds improve understanding of the differential dimension in linear PDE systems.

Abstract

We prove upper and lower bounds for leading coefficient of Kolchin dimension polynomial of systems of partial linear differential equations in codimension two.