Mini-Workshop: Wellposedness and Controllability of Evolution Equations

Abstract

This is the extended abstract of a talk announcing results obtained in collaboration with Thomas Duyckaerts. Since the seminal work of Russell and Weiss in 1994, resolvent conditions for various notions of admissibility, observability and controllability, and for various notions of linear evolution equations have been investigated intensively, sometimes under the name of infinite-dimensional Hautus test. This paper sets out resolvent conditions for null-controllability in arbitrary time: necessary for general semigroups, sufficient for analytic normal semigroups. The proofs are based on the so-called ''control transmutation method'' and a new version of the ''direct Lebeau-Robbiano strategy''. The improvement of this strategy also yields interior null-controllability of new logarithmic anomalous diffusions.