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arXiv · 2509.02814

Integrated Semigroups for abstract differential-algebraic equations

Mehmet Erbay·Birgit Jacob·Timo Reis
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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 $\frac{d}{d t}x=Ax$, 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.

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Mehmet Erbay, Birgit Jacob, Timo Reis. 2025-09-02. Integrated Semigroups for abstract differential-algebraic equations. https://arxiv.org/abs/2509.02814

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