# Semigroups associated with differential-algebraic equations

## TL;DR

This paper investigates conditions under which differential-algebraic equations in infinite-dimensional spaces can be associated with $C_{0}$-semigroups, focusing on initial value spaces and operator pencils with polynomially bounded resolvents.

## Contribution

It characterizes the existence of $C_{0}$-semigroups for infinite-dimensional differential-algebraic equations and identifies the appropriate initial value spaces.

## Key findings

- Identifies conditions for associating $C_{0}$-semigroups with such equations.
- Characterizes the initial value space for these equations.
- Analyzes operator pencils with polynomially bounded resolvents.

## Abstract

We consider differential-algebraic equations in infinite dimensional state spaces and study, under which conditions we can associate a $C_{0}$-semigroup with such equations. We determine the right space of initial values and characterise the existence of a $C_{0}$-semigroup in the case of operator pencils with polynomially bounded resolvents.