On higher index differential-algebraic equations in infinite dimensions

2017/10/24 by Trostorff, Sascha, Waurick, Marcus · 2 citations
#34A09 #34A12 #34A30 #34G10 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1710.08750

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.

Cited by

• Evolutionary equations with state-dependent delay
• Integrated Semigroups for abstract differential-algebraic equations

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