Integrated Semigroups for abstract differential-algebraic equations

2025/09/02 by Erbay, Mehmet, Jacob, Birgit, Reis, Timo · 1 citation
#34A09 #34G20 #47D06 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2509.02814

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 (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.

Citations

• A pseudo-resolvent approach to abstract differential-algebraic equations
• On solvability of dissipative partial differential-algebraic equations
• A linear relation approach to port-Hamiltonian differential-algebraic equations
• Semigroups associated with differential-algebraic equations
• On higher index differential-algebraic equations in infinite dimensions
• The index of general nonlinear DAEs

Cited by

• Differential algebraic system nodes

Related

• On the Weierstraß form of infinite dimensional differential algebraic equations
• Semigroups associated with differential-algebraic equations
• A pseudo-resolvent approach to abstract differential-algebraic equations
• On Differential-Algebraic Equations in Infinite Dimensions
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