On higher index differential-algebraic equations in infinite dimensions

Trostorff, Sascha and Waurick, Marcus; Böttcher, Albrecht and Potts, Daniel and Stollmann, Peter and Wenzel, David, eds. (2018) On higher index differential-algebraic equations in infinite dimensions. In: The Diversity and Beauty of Applied Operator Theory. Operator Theory: Advances and Applications, 268 . Springer, DEU, pp. 477-486. ISBN 9783319759951 (https://doi.org/10.1007/978-3-319-75996-8_27)

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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.