Integrated Semigroups for abstract differential-algebraic equations

Abstract

We study integrated semigroups for infinite-dimensional differential-algebraic equations (DAEs) admitting a resolvent index. Building on the notion of integrated semigroups for the abstract Cauchy problem $\frac{d}{dt}x=Ax$, we extend this concept to the DAE setting. The resulting framework is used to analyze inhomogeneous DAEs and plays a central role in characterizing their solutions.