  In this article we investigate the solvability of infinite-dimensional
differential algebraic equations. Such equations often arise as partial
differential-algebraic equations (PDAEs). A decomposition of the state-space
that leads to an extension of the Hille-Yosida Theorem on Hilbert spaces for
these equations is described. For dissipative partial differential equations
the famous Lumer-Phillips generation theorem characterizes solvability and also
boundedness of the associated semigroup. An extension of the Lumer-Phillips
generation theorem to dissipative differential-algebraic equations is given.
The results is illustrated by coupled systems and the Dzektser equation.

Functional Analysis;Analysis of PDEs;Optimization and Control