Project Area A: Analysis of infinite-dimensional pH systems

An infinite-dimensional system can be formulated mathematically as an equation on an infinite-
dimensional vector space. This includes partial differential equations, partial differential alge-
braic equations, delay equations, and combinations thereof. Thus, a wide variety of phenom-
ena such as sound, heat, electrostatics, electrodynamics, fluid dynamics, population dynamics,
elasticity, or quantum mechanics can be similarly formalized in terms of infinite-dimensional
pHS.

Within this project area, project A01 studies infinite-dimensional pH-DAEs, project A02 in-
vestigates a pH-formulation of the Vlasov-equation arising from the mean-field limit of interact-
ing particle systems, and projects A03, A04 and A05 examine infinite-dimensional pH-PDEs.

The projects A01, A03 and A05 use methods from contraction semigroups and operator
theory and thus have a methodological focus in common. Projects A01, A03, A04 and A05
have a methodological link via differential-algebraic structures.