Speaker
Description
We explore a class of port-Hamiltonian partial differential algebraic equations (pH-pDAEs), characterized by a self-adjoint linear relation and a skew-adjoint operator. We parametrize all their self-adjoint and skew-adjoint realizations making use of extension theory of symmetric relations. To this end, we explicitly construct a boundary triplet for a class of linear relations in range representation defined by two matrix differential operators on one-dimensional spatial domains. This immediately enables us to formulate the corresponding port-Hamiltonian system dynamics via differential inclusions that fits into the classical geometric framework. The proposed methodology is demonstrated through applications to the Dzektser equation and an elastic rod model with non-local elasticity condition.
