On higher index differential-algebraic equations in infinite dimensions

TL;DR

This paper investigates initial value problems for differential-algebraic equations in infinite-dimensional Hilbert spaces, establishing existence, uniqueness, and classical solutions under certain conditions.

Contribution

It introduces a growth condition for operator pencils and constructs nested subspaces to obtain classical solutions, advancing the theory in infinite-dimensional settings.

Findings

Proves existence and uniqueness of solutions under growth conditions.

Constructs nested subspaces for classical solutions.

Extends DAE theory to infinite-dimensional Hilbert spaces.

Abstract

We consider initial value problems for differential-algebraic equations in a possibly infinite-dimensional Hilbert space. Assuming a growth condition for the associated operator pencil, we prove existence and uniqueness of solutions for arbitrary initial values in a distributional sense. Moreover, we construct a nested sequence of subspaces for initial values in order to obtain classical solutions.