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

Abstract dissipative Hamiltonian differential-algebraic equations are everywhere