  In this paper we study the representation of partial differential equations
(PDEs) as abstract differential-algebraic equations (DAEs) with dissipative
Hamiltonian structure (adHDAEs). We show that these systems not only arise when
there are constraints coming from the underlying physics, but many standard PDE
models can be seen as an adHDAE on an extended state space. This reflects the
fact that models often include closure relations and structural properties. We
present a unifying operator theoretic approach to analyze the properties of
such operator equations and illustrate this by several applications.
