Olga Aryasova (Inst. of Geophysics, Nat. Acad. of Sciences of Ukraine / Friedrich–Schiller–Univ. Jena)
Christian Seifert (Technische Universität Hamburg)
Abstract: Given an abstract Cauchy problem in a Banach space we consider two questions:
1. Can we steer the system to any given state (or to zero, say) in finite time by some inhomogeneity?
2. Can we extract information on the final (or initial) state by just measuring the trajectory of the state?
These two questions are classical in mathematical systems theory and it is well-known that they are related by duality.
In this talk we will first give an overview on this duality and then turn to recent results on answering these questions in Banach spaces, which can then be applied to parabolic partial differential equations on unbounded domains.
The talk is based on joint works with CLemens Bombach (Chemnitz), Michela Egidi (Rostock), Dennis Gallaun (Hamburg) and Martin Tautenhahn (Leipzig).