Well-posedness and semigroup theory

Organisers: Ruth Curtain (Groningen), Birgit Jacob (Dortmund), Hans Zwart (Twente)

A large class of partial differential equations (pde) -- in particular, pde's with control acting through the boundary and pde's where the measurements can only be taken at few points --- can be represented as a well-posed linear system. This general approach can then be used to formulate and study properties like controllability, observability and admissibility. An essential component of a well-posed linear system is a strongly continuous semigroup of operators. Moreover, the whole system itself has a semigroup represention. Consequently, there is a natural link between semigroup theory and well-posedness. Of particular interest are the following subclasses of well-posed linear systems: passive systems, dissipative systems, reciprocal systems and boundary control systems in factor form.

Speakers: Titles

Charles K. Batty, Oxford: What does the shape of the pseudospectra of a semigroup generator imply?

Zbigniew Emirsajlow: On admissible input elements for the implemented semigroup.

Klaus-Jochen Engel, L'Aquila: Well-posedness of Cauchy problems with Wentzell boundary conditions

Birgit Jacob, Dortmund: When is an observability operator admissible?

Susanna Piazerra, Tuebingen: What can semigroups do for delay equations?

Hans Zwart, Twente: Is $A^{-1}$ an infinitesimal generator?

Written by Stuart Townley
Last modified: January 2003